Dragon Age: Origins crashes more frequently on modern PCs. One thing that can reduce the number of crashes is to use something called NTCore 4GB Patch, which allows old applications to use more RAM. I can't link to it due to forum rules about, but you can find it via Google.
You can find more info and instructions on the Dragon Age Origins page on the website PC Gaming Wiki.
If that patch reduces your crashes, I would also like to add that it's a good idea to save the game and relaunch during long sessions. The game has a memory leak and crashes more often the longer you're playing.
