Running an 8 year old I have become something of an expert on this subject - to the extent that even if he's out I find myself watching cartoons now and he is starting to tell me I am a bit sad
To be fair a lot of them are on the children's cable/satellite channels in particular Tom & Jerry, Scooby Doo (don't dismiss 'Be Cool Scooby Doo' as I actually think its at least as good as the 'classic' ones and better than the 80's ones) and Bugs and Daffy are often on as well. Sadly not Roadrunner though which can still actually make me laugh out loud - again
I'm a fan of some of the new ones just as much though - Phineas & Ferb for example is now one of my all time favourite cartoons.
One I do miss that is never shown now is Pinky And The Brain though, a brilliant cartoon.
On a vaguely related topic, get Laurel And Hardy back on TV!