Christian is talking about problems with suspend-to-RAM and suspend-to-disk and the major cause of issue being the non-free Conexant HSF modem driver.
Since I got my new laptop I had my share of issues with suspend-to-*.
At the beginning everything worked fine, out of the box. Then (I think) I realized that my video card (damned ATI) was not working in accelerated mode, so I decided to fix that and since the card is too new to be even listed as existing on radeon driver's support page, I had to use fglrx.
Then I made the DRI work but suspend-to-ram ceased to work (after a few testing->experimental; experimental--> upstream updates, both ways); I started using the experimental driver (8.31.5-1) which proved to be stable enough (this time) just for suspend-to-disk, if it had dri enabled, or suspend-to-ram, if not having DRI enabled.
I even made a patch to help the maintainer update faster the package (I added a get-orig-source rule in debian/rules).
Now I have ported the patches in the debian package and updated it to 8.33.6 and I am running that. Problems include: consoles are not accessible, but suspend-to-ram and dri work. I will submit a bug with the patch to updated fglrx package.
I expect that I'll try soon to update to 8.34.8 in the hope that I will get all the things working: suspend-to-*, consoles, dri.