Sometimes I want to make my .gpx files anonymous because it's data that I recover by myself using OSMTracker for Android and I don't want the whole world knows when I was there.
Yeah, maybe I'm a bit crazy. Nice to meet you ;)
Today, I found  a real simple solution for this: xmlstarlet
Once you have it installed, you can excecute:
xmlstarlet ed \ -P \ -N x=http://www.topografix.com/GPX/1/1 \ -u '//x:time' \ -v 1970-01-01T00:00:00Z \ input.gpx > output-nulltime.gpx
And what will put 1970-01-01T00:00:00Z on all the <time> tags.
That's all! Now, they are ready to be uploaded to the OSM community and nobody will know where you was there :)