Hi
I think you clued us in to the problem in your first sentence. If you are like me, you copied a bunch of your old apps from the old machine into the new one, right? It is far more reasonable to think that there is a conflict within that group than that you have a RAM problem.
with the new OSX, you need the new apps that are designed to work with it. Running an old app can easily crash the system. This includes your widgets and drivers.
Kick all the stuff off your account auto start, and out of your dashboard. See if you have crashes like before. Hopefully not. Add them back one at a time until you crash. Or update them and add them as you get them.
Some of my old apps were never updated. Oh well, the new OSX is cool enough to make up for that problem.
Norton is still a problem on my machine. I have not been able to kill all the bits and pieces that were installed back in the day.
i also use an external Firewire HD with a simple system on it that is very useful to test conflicts. It is a good thing to have for backups as well.
Lastly, get Applejack. It is a cool tool to put things back in order after a crash.
http://applejack.sourceforge.net/
PS. i bragged to my friend how great OSX was after she had to reinstall her win sys - again. that i had never had to reinstall OSX. THE NEXT DAY I had to reinstall OSX. I swear, there are boogy men out to get ya every time you are over confident! Back up now!