Thanks for taking the time to report this bug.
Without a stack trace from the crash it's very hard to determine what caused it.
Can you get us a stack trace? Please see http://live.gnome.org/GettingTraces for more information on how to do so. Thanks in advance!

Installed bug buddy. However, it does not start on the crash.

That's because this is no crash but just a normal error.

Could you give details about the GStreamer (and plugins) and totem versions you use? Also does this happen for all h264 files or only this single file?

Could you run this in a terminal / on the command line, and provide the output:

    gst-launch-0.10 -v playbin2 uri=file:///path/to/file

?

Here is the terminal output.
Happens on all hi def h264 taken with my camera. Once edited and/or resized, they are OK. Worked ok previously.... 
Message: Error: Internal GStreamer error: negotiation problem.  Please file a bug at http://bugzilla.gnome.org/enter_bug.cgi?product=GStreamer.
gstffmpegdec.c(1267): gst_ffmpegdec_negotiate (): /GstPlayBin2:play/GstURIDecodeBin:uridecodebin0/GstDecodeBin2:decodebin20/ffdec_h264:ffdec_h2640:
could not find caps for codec (h264), unknown type

Could you make a small clip available on some download site (http) ?

Here is an url to a file showing the problem:
(Note: this does not happen on my laptop with Lenny, but does happen on an AMD64 with Squeeze.)
http://www.adrive.com/public/68c4cd57a6eb7dde457e4d1b7262d14d8c4ed8cf97e6d72c18a6372b06e86a5d.html

This looks like a packaging issue with the debian gstreamer0.10-ffmpeg package. Please report it in the debian bug tracker.

It works fine for me with gst-ffmpeg git (using the internal ffmpeg snapshot).

*** This bug has been marked as a duplicate of bug 626007 ***

Works fine for me with the Debian GStreamer packages... which version of libavcodec52 do you have installed? If it's the one from Debian-multimedia install the version from Debian...

It would be the one from Debian-multimedia. The problem is resolved by installing another version.