I myself have played both Shrek 2 and Shrek the Third, and while I do like both, I find the latter much more fun. The playable characters are all well done, The levels are great, the music is surprisingly good (The gift shop, Vs Cyclops, Castle Capture ver. 1, Vs the Giant Knight, Stromboli's Workshop, both prison levels, Rundown Streets and The Grand Finale being my favorites), the minigames and Castle Capture Multiplayer is also quite fun. The game even has 4 button codes for it, them being: free 10 000 coins, Secret costume 1 and 2 in addition to a bonus level in Shrek's Swamp were he rescues baby ogres. It's also very fun to speedrun through the game on either Charming or Grimm difficulty (I've done both).
The game isn't without it's flaws. Two-player co-op in Story Mode would be very good, in addition to being able to play as any character as you want after full completion of it. I'd like to have an option to refresh the quests so I could earn money more quickly. I would also like more levels and quests. Non-regenerating health should also be an option, at least for Grimm difficulty. All characters should also have at least 2 costumes. Shrek has 4 (Not counting the secret ones), everyone else have only one.
I played through Shrek the Third with my girlfriend a few months ago. It's a thoroughly serviceable action platformer, although it was clearly a movie tie-in (iirc one of the main menu options took you straight to a trailer for another Dreamworks film). Also semi-related, the Fairytale Freakdown version of Shrek won a tournament on SaltyBet recently and it really makes me want to try the original game. I say that we get Lord Ape and Lalzu to do a playthrough after the next Slam in the Swamp.
Shrek 2 for the GBA was pretty fun, and I've beaten Shrek Treasure Hunt for the PS1. For reference, Shrek Treasure Hunt came out in late 2002, making it one of the last games ever released for the console. It's also one of the worst.
I've also played the Penguins of Madagascar platformer for GBA, it's an instant classic as far as Dreamworks games go.
I rented but never finished Shrek 2 on PS2, I seem to remember a pumpkin patch level? My friend also had Over the Hedge (which has a trailer in Shrek SuperSlam), but I remember it being pretty dire. It was one of those movie tie-ins which take place after the film, the first level was the final few minutes of the film.