My vote has to be for Ratchet 2 cuz those games have been solid every time.

Super Mario Bros 2 took a weird twist from the first, and I definitely think the 3rd installment was one of the best Mario's ever made.

Sonic has never been my type of game since it was a bit too fast for me as a kid.

I really liked Jak 1 and 3... 2 wasnt terrible but it went a darker themed route and was actually quite difficult for me as a kid.

I'd go
1. Ratchet 2, one of my favorite platformers of all time, could be the best in the series

2. Super Mario Bros 2, even though it's technically not even supposed to be a mario game it still had a lot of influence on the series as a whole. If it weren't for 2 Peach wouldn't float and Luigi wouldn't be the taller brother with a weird high jump and slippery control. It's also probably my third or fourth favorite Mario game ever, and I know I am in the minority on that.

3. Jak 2, Jak's transition from silent protagonist to gun-toting, grizzled badass was jarring for me, though not as bad as the prince of persia's. Still, the game mechanics were improved and it turned into a better game than its predecessor.

4. Sonic, I was never a big sonic fan personally.

Play the original Jak & Daxter for the PS2.........then stop! I wish I would have done the same thing!

On reflection the best jak and daxter game was the first. But R&C got better with each successive game at least on PS2 and the main games on PS3 were also great.

Ratchet & Clank 2
Sonic 2
Jak 2
Mario 2

We talking Doki Doki Panic or Lost Levels here? I see you mean Doki Doki Panic but I don't really consider that a Mario game :P

Either way, Sonic 2 is a classic (even though it has a terrible continue system and some cheap design) so I will go with that one...

Ratchet and Clank Going Commando
Sonic the Hedgehog 2
Jak 2
Super Mario Bros 2

Why? I have heard very mixed impressions about this trilogy. Besides I like to play things before I judge them!

 I wasn't personally a huge fan of the fact that the franchise became similar to GTA with Jak II.  Who knows! Maybe you would like Jak II more than me!

Indeed....... I think Jak 1 was an instant classic, but the change up of Jak 2 was so left field, I played it and played it. It was awesome. 

Riding aroung the city causing havoc was such a fun experience. lol