On the PS2 the list is immense.... pick a genre and I can name at least a couple of fantastic games.
But some of my favorites!
Dragon quest VIII Journey of the cursed king.
Gran Turismo 3 and 4
Tekken (ALL of them.)
Katamari 1 and 2
King's Field The Ancient City (This one might be tough to find... and the book for it is also hard to find, expect to pay out the nose....
http://www.amazon.com/Kings-Field-Ancient-City-Playstation-2/dp/B00006599W )
Twisted Metal Black
Just so many greats on the PS2!
On the Wii there is less but some awesome games on it non the less.
Kororinpa Marble Mania, if you like puzzle games. This one makes fantastic use of motion controls.
WarioWare Smooth moves!!!
Excite Truck gets a vote from me. (I didn't really care for excite bots even though everyone else says its the better of the two.)
New Super Mario bros (If you don't like 2D platformers you might not like it.)
Resident Evil 4 (It's also on the PS2 and it is awesome but the Wii's controls actually make it even better. I might also mention its really the only RE game I like... lol)
I could go on all day about the two systems, but this list alone would keep some one busy for at least a month even if you played 24/7.
Edit: About the Kings Field strategy guide, I would say it is almost required to play the game. That or expect to be visiting Youtube and Google allot to find out "What the hell, how can I get past this part?"