My system always was able to suspend and resume properly under 12.10 and 12.04 and earlier, but immediately after the 13.04 upgrade, I find it crashes on trying to return from suspend. Sometimes it just repaints part of the screen with a bit of the startup/splash graphic then halts, and sometimes it gets a bit further, blanking the screen and showing a mouse pointer - which is frozen.
Hardware is a AMD Phenom(tm) II X4 945 Processor × 4 on an nvidia motherboard, 8GB RAM, GeForce GTX 550 Ti/PCIe/SSE2/3DNOW!, running Ubuntu 13.04 32 bit.
Can't find anything that seems relevant in the system log - maybe I don't know what to look for though, even which log. I will post anything requested.