<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>111 - Disclosure - Other Current Assets</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>4</Level><ElementName>us-gaap_OtherCurrentAssetsTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="eol_PE10315---13S-1-0008_STD_366_20121231_0" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt;
&lt;p style="MARGIN-TOP: 18px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Note 3. Other Current
Assets&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Other current
assets consisted of the following at December&amp;#xA0;31, 2012 and
2011:&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px; FONT-SIZE: 12px"&gt;
&amp;#xA0;&lt;/p&gt;
&lt;table style="BORDER-COLLAPSE: collapse" border="0" cellspacing="0" cellpadding="0" width="76%" align="center"&gt;
&lt;tr&gt;
&lt;td width="76%"&gt;&lt;/td&gt;
&lt;td valign="bottom" width="4%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td valign="bottom" width="4%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;
&lt;p style="BORDER-BOTTOM: #000000 1px solid; WIDTH: 39pt"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;Description&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: #000000 1px solid" valign="bottom" colspan="2" align="center"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;2012&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: #000000 1px solid" valign="bottom" colspan="2" align="center"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;2011&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Supplies
inventory&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;604,179&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#x2014;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred offering
costs&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;341,166&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#x2014;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Prepaid expenses&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;132,201&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;124,773&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="FONT-SIZE: 1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;1,077,546&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;124,773&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="FONT-SIZE: 1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Supplies
inventory at December&amp;#xA0;31, 2012 includes reagents and supplies
that will be used to manufacture Tcelna and placebo product in
Opexa&amp;#x2019;s Phase IIb clinical study. Opexa expects to amortize
these prepaid reagents and supplies to research and development
costs in the consolidated statements of expenses over the course of
the clinical study.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred
offering costs at December&amp;#xA0;31, 2012 include costs incurred
from third parties in connection with the implementation of an
at-the-market program (&amp;#x201C;ATM Agreement&amp;#x201D;) in September
2012 pursuant to which Opexa may sell shares of its common stock
from time to time depending upon market demand through a sales
agent in transactions deemed to be an &amp;#x201C;at-the-market&amp;#x201D;
offering as defined in Rule 415 of the Securities Act of 1933. As
of December&amp;#xA0;31, 2012, the costs of $101,972 in connection with
the implementation of the ATM Agreement were capitalized and are
included in other current assets in the consolidated balance
sheets. Upon the sales of any shares of common stock under the ATM
Agreement, the capitalized costs will be offset against the
proceeds of such sales of shares of common stock.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred
offering costs at December&amp;#xA0;31, 2012 also include costs
incurred from third parties in connection with the implementation
of a $1.5 million Purchase Agreement and a $15 million Purchase
Agreement (collectively, the &amp;#x201C;Purchase Agreements&amp;#x201D;) in
November 2012 pursuant to which Opexa has the right to sell to
Lincoln Park Capital Fund, LLC (&amp;#x201C;Lincoln Park&amp;#x201D;) an
aggregate of up to $16.5 million in shares of its common stock,
subject to certain conditions and limitations. As of
December&amp;#xA0;31, 2012, the remaining costs of $216,198 in
connection with the implementation of the Purchase Agreements
remained capitalized and are included in other current assets in
the consolidated balance sheets. Upon the sales of shares of common
stock under the Purchase Agreements, the capitalized costs are
offset against the proceeds of such sales of shares of common
stock.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred
offering costs at December&amp;#xA0;31, 2012 also include costs
incurred from third parties in connection with the Option and
License Agreement entered into with Ares Trading SA
(&amp;#x201C;Merck&amp;#x201D;), a wholly owned subsidiary of Merck Serono
S.A., on February&amp;#xA0;4, 2013. Under the terms of the Agreement,
the Company received an upfront payment of $5 million on
February&amp;#xA0;20, 2013. As of December&amp;#xA0;31, 2012, the remaining
costs of $22,996 in connection with the Option and License
Agreement remained capitalized and are included in other current
assets in the consolidated balance sheets.&lt;/font&gt;&lt;/p&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for other current assets.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Other Current Assets</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Other Current Assets</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.opexatherapeutics.com/taxonomy/role/NotesToFinancialStatementsOtherCurrentAssetsTextBlock</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>1</NumberOfRows></InstanceReport>
