I'm also running Cyanogenmod 6 (6.0.0-DS-RC2) and it runs fine for me, until I fill up the memory a little too much. The system needs a little breathing room (for cache/swap). If you're on CM6-RC1, I would suggest upgrading to RC2 (or higher, if a newer version is out by the time you get around to it). I also had a good deal of issues with CM6-RC1, so it sounds like that might be what you're running. What may also help you curb your memory issues is using FireRat's Apps2SD script. You have to copy the script file to your SD card and run it from the Terminal app (as root). BEWARE, however, that if you aren't careful with how you use the script, you will find yourself restoring and reinstalling all of your apps (I recommend using AppBrain, it can save you a lot of hassle of trying to remember what apps you had installed; it saved my butt more than once when this happened to me).
In my experience, CyanogenMod 5.0.8 ran best, but CyanogenMod 6 has lots of fun FroYo features, so I like it much better. Plus, they're still improving CM6, so it will only get better. They might even get a proper Apps2SD going on CM6 someday (Apps2SD support is much better on CM5.0.8).