algorithm2e package: print caption without text "Algorithm <number>:"

Adjust the way the caption text is set. Since algorithm2e overrides the way \captions are handled (to have absolute control over placement and embellishments (like rules above/below), add the following to your preamble after loading algorithm2e:

\makeatletter
\renewcommand{\algocf@captiontext}[2]{\AlCapNameSty{\AlCapNameFnt{}#2\endgraf}}%
\makeatother

The above snippet was modified from the source - algorithm2e.sty - by removing the formatting of the first argument #1 (the Algorithm < num >: part). You'll see there's no reference to it, and only the second argument #2 is used.

\documentclass{beamer}

\usepackage[linesnumbered,boxed,ruled,vlined]{algorithm2e}

\makeatletter
\renewcommand{\algocf@captiontext}[2]{\AlCapNameSty{\AlCapNameFnt{}#2\endgraf}}%
\makeatother

\begin{document}

\begin{frame}
  \begin{center}
    \begin{algorithm}[H]
      \DontPrintSemicolon
      \KwIn{
        array $v[0, \dots, n-1]$,
          $n \geq 1$
      }
      \KwOut{sum of odd entries of $v$}

      $s \gets 0$\;

      \For{$(i \gets 0; i < n; i{+}{+})$}{
        \If{$v[i] \bmod 2 = 1$}{
          $s \gets s + v[i]$\;
        }
      }
      \Return $s$\;
      \caption{$\mathtt{Add}(v, n)$}
    \end{algorithm}
  \end{center}
\end{frame}

\end{document}