Is it possible to have connecting loop lines (like algorithm2e) in algorithmic?

Here is one way of doing it using algorithmicx - more advanced yet similar to and compatible with algorithmic. It involves expanding and contracting a token list \thelines that keeps track of the nested level. At every new level, an additional \theline is added to \thelines.

\documentclass{article}
\usepackage{algorithm}% http://ctan.org/pkg/algorithm
\usepackage{algpseudocode}% http://ctan.org/pkg/algorithmicx

\makeatletter
% This is the vertical rule that is inserted
\def\therule{\makebox[\algorithmicindent][l]{\hspace*{.5em}\vrule height .75\baselineskip depth .25\baselineskip}}%

\newtoks\therules% Contains rules
\therules={}% Start with empty token list
\def\appendto#1#2{\expandafter#1\expandafter{\the#1#2}}% Append to token list
\def\gobblefirst#1{% Remove (first) from token list
  #1\expandafter\expandafter\expandafter{\expandafter\@gobble\the#1}}%
\def\LState{\State\unskip\the\therules}% New line-state
\def\pushindent{\appendto\therules\therule}%
\def\popindent{\gobblefirst\therules}%
\def\printindent{\unskip\the\therules}%
\def\printandpush{\printindent\pushindent}%
\def\popandprint{\popindent\printindent}%

%      ***      DECLARED LOOPS      ***
% (from algpseudocode.sty)
\algdef{SE}[WHILE]{While}{EndWhile}[1]
  {\printandpush\algorithmicwhile\ #1\ \algorithmicdo}
  {\popandprint\algorithmicend\ \algorithmicwhile}%
\algdef{SE}[FOR]{For}{EndFor}[1]
  {\printandpush\algorithmicfor\ #1\ \algorithmicdo}
  {\popandprint\algorithmicend\ \algorithmicfor}%
\algdef{S}[FOR]{ForAll}[1]
  {\printindent\algorithmicforall\ #1\ \algorithmicdo}%
\algdef{SE}[LOOP]{Loop}{EndLoop}
  {\printandpush\algorithmicloop}
  {\popandprint\algorithmicend\ \algorithmicloop}%
\algdef{SE}[REPEAT]{Repeat}{Until}
  {\printandpush\algorithmicrepeat}[1]
  {\popandprint\algorithmicuntil\ #1}%
\algdef{SE}[IF]{If}{EndIf}[1]
  {\printandpush\algorithmicif\ #1\ \algorithmicthen}
  {\popandprint\algorithmicend\ \algorithmicif}%
\algdef{C}[IF]{IF}{ElsIf}[1]
  {\popandprint\pushindent\algorithmicelse\ \algorithmicif\ #1\ \algorithmicthen}%
\algdef{Ce}[ELSE]{IF}{Else}{EndIf}
  {\popandprint\pushindent\algorithmicelse}%
\algdef{SE}[PROCEDURE]{Procedure}{EndProcedure}[2]
   {\printandpush\algorithmicprocedure\ \textproc{#1}\ifthenelse{\equal{#2}{}}{}{(#2)}}%
   {\popandprint\algorithmicend\ \algorithmicprocedure}%
\algdef{SE}[FUNCTION]{Function}{EndFunction}[2]
   {\printandpush\algorithmicfunction\ \textproc{#1}\ifthenelse{\equal{#2}{}}{}{(#2)}}%
   {\popandprint\algorithmicend\ \algorithmicfunction}%
\makeatother

\begin{document}

\begin{algorithm}
  \caption{Euclid’s algorithm}\label{euclid}
  \begin{algorithmic}[1]
    \Procedure{Euclid}{$a,b$}\Comment{The g.c.d.\ of a and b}
      \LState $r\gets a\bmod b$
      \While{$r\not=0$}\Comment{We have the answer if r is 0}
        \LState $a\gets b$
        \LState $b\gets r$
        \LState $r\gets a\bmod b$
      \EndWhile\label{euclidendwhile}
      \LState \Return $b$\Comment{The gcd is b}
    \EndProcedure
  \end{algorithmic}
\end{algorithm}
\end{document}

Every single definition is redefined to now manage the indentation:

• At the start of every block, you insert \printindent and append \pushindent. This removes the regular algorithmic indent \algorithmicindent and prints the vertical rule. At the end it adds another indent so that subsequent statements are properly indented; and
• At the end of every block, you insert \popindent\printindent. This removes the regular algorithmic indent \algorithmicindent, then swallows one indent, and prints the remaining indents.

I've added some additional macros like \printandpush and \popandprint to combine the above \printindent, \pushindent and \popindent modifications.

Instead of using the traditional \State for procedural statements, use \LState. It performs a similar task to what is mentioned above.

This solution should work well for the standard environments defined about. However, other more complicated environments defined using \algdef may require more fiddling to obtain correct indentation.

Regarding the vertical rule. It is set at .5em from the left-most margin of the block, is .4pt wide and is defined by \therule:

\def\therule{%
  \makebox[\algorithmicindent][l]{%
    \hspace*{.5em}\vrule height .75\baselineskip depth .25\baselineskip}}%

Token list appending is described in How does one append material to a token list?, while token removal is discussed in How does one remove material from a token list?