I am running openSUSE 13.1 for a week now without any problems. This is a fresh install. This morning I installed an update for xorg, since then X randomly crashes, e.g. when using chrome to access facebook, google searches, ...
Here is what I could find in the logs: https://dl.dropboxusercontent.com/u/6669000/Xorg.0.log

UPDATE: below are the last updates that were applied:
xorg-x11-server-7.6_1.14.3.901-4.1.x86_64 Sat 28 Dec 2013 06:44:42 AM CET
openssl-1.0.1e-11.5.1.x86_64 Thu 26 Dec 2013 06:51:58 PM CET

so the xorg update is the culprit