Sims 2 requires 2.5, but you can play it from a 2.0 using a program called PSPsetX.
Here's a list from a Spanish forum of games that are not compatible with 1.5 in any way, I've tried to translate it, notice that some games not on this list need to use some trick for them to work in a 1.5:
Not working (versiones europeas o americanas)
Grand Theft Auto Liberty City Stories
Lemmings (final version, beta works )
Peter Jackson King Kong
Pinball Hall of Fame
Rockman X Irregular Hunter // Requires 2.5 //
Smackdown vs. Raw 2006
Socom Fireteam Bravo
The Sims 2
Not working (versiones asiaticas)
Byte Hell 2000 (JAP)
Exit (JAP) // Requiere 2.5 //
Katamari Damacy (JAP)
Monster Hunter Portable (JAP)
Piposaru Academia 2 (JAP)
Shin Megami Tensei Devil Summoner (JAP)
Street Fighter Zero 3 Double Upper (JAP) // Requiere 2.5 // (no music en 2.0)
Vulcanus Seek and Destroy (KOR)
Work but don't save the game
Crash Tag Team Racing (USA / JAP) (Hay que aplicarle el Fix)
Daisenryaku Portable (JAP)
Geki Sengoku Musou (JAP)
Go! Sudoku
Harvest Moon Boy And Girl (JAP)
Jet de Go
Metal Gear Ac!d 2
Pac Man World 3 (se cuelga en el primer nivel)
Practical Intelligence Quotient
Tokobot / Karakuri (original, parcheado sí salva)
World Championship Poker 2
Work with trouble in somes levels (but save)
Harry Potter and the Goblet of Fire
Lord of the Rings Tactics
Need for Speed Underground Rivals EUR (hangs while playing)