Label in a footnote in author's field causes 'xfootnotemark doesn't match its definition'

You could save the footnote counter and use it for the second author in the following way:

\documentclass{article}
\newcounter{savecntr}% Save footnote counter
\newcounter{restorecntr}% Restore footnote counter
\author{Gopal \setcounter{savecntr}{\value{footnote}}\thanks{XYZ University} ,
Someone else \thanks{ABC University} ,
Another \setcounter{restorecntr}{\value{footnote}}%
  \setcounter{footnote}{\value{savecntr}}\footnotemark% Print footnotemark
  \setcounter{footnote}{\value{restorecntr}} ,
Last author \thanks{IJK College}}
\title{My title}
\begin{document}

\maketitle

Here is some text.
\end{document}
​

The idea here is to store the footnote counter before reusing the affiliation, and then to restore it after you've used it so that subsequent authors receive a different (unique) \footnotemark.

Since you are using hyperref, using \footnotes as well and wanting to reference them is tricky. On the one hand, the regular titling command \author does one of two things, neither of which helps with footnotes: It typesets the contents in a tabular - a known issue that traps footnotes - and temporarily redefines the way \footnote works (by executing \let\footnote\thanks). On top of this, the hyperref README suggests the downside when "re-using a \footnotemark out of order/sequence":

The footnote support is rather limited. It is beyond the scope to use \footnotemark and \footnotetext out of order or reusing \footnotemark. Here you can either disable hyperref's footnote support by hyperfootnotes=false or fiddle with internal macros, nasty examples...

The example that follows works with modifying both the traditional footnote counter, as well as hyperref's internal Hfootnote counter. The "nasty example" makes things work, but it remains "nasty":

\documentclass{article}
\usepackage[hyperfootnotes]{hyperref}% http://ctan.org/pkg/hyperref
\newcounter{savecntr}% Save footnote counter
\newcounter{restcntr}% Restore footnote counter
\newcounter{Hsavecntr}% Save Hfootnote counter
\newcounter{Hrestcntr}% Restore Hfootnote counter

\begin{document}

\makeatletter
\begingroup
  \let\footnotesize\small \let\footnoterule\relax% Set footnote parameters
  \renewcommand\thefootnote{\@fnsymbol\c@footnote}% Style of footnotes: symbols
  \vskip 60\p@
  \begin{center}%
    {\LARGE My title \par}%
    \vskip 3em%
    {\large
      \lineskip .75em%
      \setcounter{savecntr}{\value{footnote}} \setcounter{Hsavecntr}{\value{Hfootnote}}% Save counters
      Gopal \footnote{XYZ University} ,% First author
      Someone else \footnote{ABC University} ,% Second author
      \setcounter{restcntr}{\value{footnote}} \setcounter{Hrestcntr}{\value{Hfootnote}}% Save restore counters
      \setcounter{footnote}{\value{savecntr}} \setcounter{Hfootnote}{\value{Hsavecntr}}% Restore similar counter
      Another \footnotemark ,% Print footnotemark with third author
      \setcounter{footnote}{\value{restcntr}} \setcounter{Hfootnote}{\value{Hrestcntr}}% Restore original counters
      Last author \footnote{IJK College}% Last author
    \par}%
  \vskip 1.5em%
  {\large \@date \par}%       % Set date in \large size.
  \end{center}\par
\endgroup
\setcounter{footnote}{0}%
\makeatother

Here is some text.\footnote{Here's a footnote.}
\end{document}

The definition of the title, author and date was taken from article.cls

As noted in the other answer, LaTeX not only uses symbols rather than numbers to produce footnote marks in the title area (i.e, title, author(s), and date) but also "gobbles" some relevant information when producing the footnotes. This makes it impossible for the hyperref package to create hyperlinks from the footnote marks to the corresponding footnotes.

If you have several co-authors and all you are trying to achieve is to avoid repeated footnotes indicating the same affiliation(s) for two or more of the co-authors, it's not worth it (IMHO) to go to a lot of trouble to program up LaTeX's footnote markers. Instead, something like the following MWE should satisfy nearly all needs. The example employs the fact that in LaTeX the first symbolic footnote mark is a raised asterisk (*) and the second is a \dagger.

The MWE also demonstrates that the \footnote and \thanks commands both generate symbolic footnotes in the title area. Once you're past the title area, footnote numbering uses arabic numerals, as expected. Happy TeXing!

\documentclass{article}
\usepackage[colorlinks=true]{hyperref}
\setlength\textheight{5.5cm} % just for this example

\title{Some Title}
\author{AuthOne\footnote{University A.} % note use of "\footnote"
  \and AuthTwo\thanks{University B.} 
  \and AuthThree$^*$ 
  \and AuthFour$^\dagger$}
\date{} % suppress 'date'

\begin{document}
\maketitle   
Hello World.\footnote{More random text.}
\end{document}