Spyro 1 and 2
Banjo Kazooie and Banjo Tooie via XBOX 360: Took me two days to complete the first one, took me two weeks to complete the second one. 0-o
Sly 2: Band of Thieves (With some help from my brother,I've beaten the main game, my brother went and looked for all the clue bottles I missed while I played other games)
Jak and Daxter 1
Valkyria Chronicles, beating the game without worrying about getting an A rank in every mission isn't too bad, but getting an A rank in every mission in the game, including all the skirmishes, was no easy feat. Had to save scum like a mad man. Heck, I think I may have done it one time without ever using orders, as I feel those break the game.
Pretty much all the games on Kirby's Dream Collection (with the exception of the first one, as my brother played and beaten that game, but for whatever reason, we were unable to reset the game so I could play it)
Journey: You'd be surprised at how much stuff you can miss in that game on your first playthrough.