The PS2 library is as deep as it is wide, and like Sinfamy said, your picks are definitely some of the best known games on the system.
So here's an alternate list for you, of games that are similar but lesser known than what you've named:
In addition to Burnout 3, why don't you try:
Burnout 2 (I prefer this over 3, for the intensity of chaining burnouts, and shorter but sweeter campaign, plus it doesn't have any EA nonsense in it)
Need for Speed Hot Pursuit 2 (possibly one of the most addictive and mechanically pure Need For Speeds ever made, it's easy to lose this in the shitpile that is NFS)
In addition to God Hand, why don't you try:
Urban Reign (This is a really fun beat em up that is kind of like Die Hard Arcade meets Tekken.
The Warriors (Rockstar's seminal installment in the beat em up genre, the combat is accessible and deep without going over the top. Very faithful to the film too, if you care about that kinda thing)
Bujingai (Devil May Cry run through the filter of JRock and Wuxia martial arts, it is a very flashy, very flamboyant hack and slash you don't wanna miss)
In addition to Silent Hill/ FF/ Rule of Rose (good luck buying that one!):
Echo Night Beyond (this a precursor to modern walking horror-lite simulators that are so popular today... you explore a space station full of ghosts both sad and vengeful)
Ghosthunter (less of a horror game and more of a grindhouse action game, this graphically impressive spooky adventure from SCE Cambridge is hell of a lot of fun)
X Files: Resist or Serve (a completely unsung game, it is actually very mechanically sound in the vein of the old Resident Evils... and faithful to the show if you have any interest)
RPGs that aren't always mentioned:
Sakura Wars: So Long My Love (more of an SRPG, that has visual novel elements, but it's historical fantasy with mecha, and in a way if you like Front Mission or Valkyria Chronicles you might like this)
Radiata Stories (a hilariously lighthearted, sweet JRPG with wonderfully charming characters and a semi open world... one of Tri Ace's best unsung games)
Wild Arms V (a very shounen western themed JRPG with beautiful graphics and a unique hexagon based combat system. The last in the series. Did I mention how unironically shounen this game is?)
SMT III: Nocturne (not exactly unsung, but amidst all the modern googaaing over its spinoff cousin Persona and the original series move to handheld, this is the last great and incredibly difficult console SMT proper)
Shadow Hearts: From the New World (You like JRPGs? a combat system based on Wheel of Fortune? How about Prohibition Era America, filter through the most un-PC Japanese lens possible? If yes, this game is for you!)
Finally, some unique ones that nobody ever talks about:
Skygunner (a difficult to master, charmingly anime, star fox esque aerial shooter that deserves a second look)
Ace Combat: The Belkan War (everyone knows Ace Combat, but this lost installment is actually one of the best. Featuring memorable characters and a sweet spanish guitar soundtrack, don't let this one slip you by)
GrimGrimoire (one of Vanillaware's lost classics, this is a magical academy themed, one of a kind side scrolling vertical battlefield RTS. The characters are sweet enough to give you cavities and of course there's time travel)
Way of the Samurai/2 (unlike most western, modern open world games, this one has a time limit over a number of days, and where you are and who you kill at any given time has serious impact on the story. PLAY IT)
