A completely different approach from Werner's one.
Load calc package and add
\makeatletter
\def\myex{\setlength{\parindent}{-\leftmargin+\labelsep}\@ifnextchar [{\@ex}{\item}}
\makeatother
in the preamble.
Then use the newly defined \myex inside the exe environments where you want the special layout, e.g.
\documentclass{article}
\usepackage[ngerman]{babel}%dt.Silbentrennung
\usepackage{gb4e,calc}
\makeatletter
\def\myex{\setlength{\parindent}{-\leftmargin+\labelsep}\@ifnextchar [{\@ex}{\item}}
\makeatother
\begin{document}
\noindent Usual layout:
\begin{exe}
\ex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
\ex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
csdf csdf % ideally, this line starts where the opening bracket starts
\end{exe}
\noindent Modified layout:
\begin{exe}
\myex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
\myex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
csdf csdf % ideally, this line starts where the opening bracket starts
\end{exe}
\end{document}
Output:

Otherwise, you can simply add a line
\setlength{\parindent}{-\leftmargin+\labelsep}
just after \begin{exe} when you want the special layout.
Of course, with this approach, items after the nineth will look like

If you don't like this behavior, you can substitute the above code between \makeatletter and \makeatother with the following one:
\newlength{\digitlen}
\settowidth{\digitlen}{1}
\makeatletter
\def\myex{%
\ifnum\thexnumi>8%
\ifnum\thexnumi>98%
\setlength{\parindent}{-\leftmargin+\labelsep-2\digitlen}%
\else%
\setlength{\parindent}{-\leftmargin+\labelsep-\digitlen}%
\fi%
\else%
\setlength{\parindent}{-\leftmargin+\labelsep}%
\fi%
\@ifnextchar [{\@ex}{\item}}
\makeatother
Thus, the following MWE
\documentclass{article}
\usepackage[ngerman]{babel}%dt.Silbentrennung
\usepackage{gb4e,calc}
\newlength{\digitlen}
\settowidth{\digitlen}{1}
\makeatletter
\def\myex{%
\ifnum\thexnumi>8%
\ifnum\thexnumi>98%
\setlength{\parindent}{-\leftmargin+\labelsep-2\digitlen}%
\else%
\setlength{\parindent}{-\leftmargin+\labelsep-\digitlen}%
\fi%
\else%
\setlength{\parindent}{-\leftmargin+\labelsep}%
\fi%
\@ifnextchar [{\@ex}{\item}}
\makeatother
\begin{document}
\setcounter{exx}{8}
\begin{exe}
\myex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
\myex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
csdf csdf % ideally, this line starts where the opening bracket starts
\end{exe}
\setcounter{exx}{98}
\begin{exe}
\myex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
\myex asdf asdf
bsdf bsdf % ideally, this line starts where the opening bracket starts
csdf csdf % ideally, this line starts where the opening bracket starts
\end{exe}
\end{document}
yields

setlistso elaborate. This is very interesting. – azetina Nov 08 '13 at 20:47resume=exeto the keylist to continue enumeration of the examples throughout the document. – Sašo Živanović Nov 08 '13 at 21:17exeto usemyexe. I don't have enough experience with usage ofg4beto advocate that. – Werner Nov 08 '13 at 21:41{exe} {exe} {myexe} \item \item {exe}.The correct numbering should be (1) (2) (3) (4) (5). – Alan Munn Nov 08 '13 at 21:57labelsepto 0 it worked. But there is a minor problem. When I "built" the preamble with\usepackage{gb4e,enumitem,calc},myexeand "the following patch" I didnt get the continuous numbering Alan Munn pointed out. Currently,myexeaffects the following numbers of ´exe´, but it is not affected by ´exe´ nor by previous ´myexe´. Each ´myexe´ starts with number 1. However, ´myexe` needs to be numbered according to its position. Is there a way to make it fit, e.g. being sensitive for previous and following ´exe´ and ´myexe´ (without manual adjustment)? – Philip Nov 09 '13 at 14:09exxis greater than 9, then the label ofmyexeis printed differently from itsexecounterpart. I think you should deletealign=left. – karlkoeller Nov 09 '13 at 16:48