In addition to bug fixing, the several free DLC packs (now all combined into one big download) added the ability to restart races, a day/night cycle and weather system (AKA fog), motorcycles, better color coding on superjumps and billboards(making them easier to see when speeding about), extra online freeburn modes (like Marked Man and Road Rage), more online co-op and competitive challenges, and custom soundtracks and trophy support for the PS3.
The paid DLC stuff is also worth a look. This includes several car packs, Cops vs Robbers mode (kind of like one flag CTF in cars), and the Big Surf Island add-on area.
Everything Criterion made DLC-wise for Burnout Paradise, free and paid both, improved upon an already fun game. The fact that Criterion supported their game for two full years after release is pretty damned awesome if you ask me. If they didn't eventually have to move on to other projects, they'd probably still be tinkering with it.