20 good games.

1. Grand Theft Auto San Andreas

2. Grand Theft Auto Vice City Stories

3. Tenchu Kurenai

4. beatmania IIDX 3rd Style

5. Pop'n Music 10

6. Dance Dance Revolution/Dancing Stage SuperNOVA (any region)

7. Dancing Stage Fusion

8. Bully/Canis Canem Edit

9. Gran Turismo 4

10. Minna Daisuki Katamari Damacy

11. Initial D Special Stage

12. Final Fantasy XII

13. Tekken 5

14. Virtua Fighter 4: Evolution

15. beatmania IIDX RED

16. Dance Dance Revolution Extreme (US)

17. Pop'n Music IROHA

18. Metal Gear Solid 3: Subsistence

19. Ghosthunter

20. Okami 

wow u must be loaded. 20 of the best games for the PS2 would easily go over $200. well here we go

God of war

God of war 2

naruto choronicles 

reisident evil 4

okami

Final Fantasy 10

Final Fantasy 10-2

Final Fantasy 12

Metal Gear Solid 2

Metal Gear Solid 3(buy substence)

Bully

racing nothing beats gran turismo 4 

Kingdom Hearts

Kingdom Hearts 2

and all kines of JRPG's 

thats all the games to get 

Keep in mind this is in no particular order...

1) Okami

2)Zone of the enders:1 and 2

3)Shin Megami Tensei: Nocturne

4)Dragon Quest VIII

5)Final Fantasy XII

6)Silent Hill 2-4 (preferrably 2)

7)Resident Evil 4

8.)Shadow of the colossus

9)Devil May cry series (1-3)

10)Disgaea: Hour of Darkness

11)Atelier Iris (1 not 2)

12)Shadow Hearts Series (1-3, very good series, not many are aware but a ps1 game, Koudelka was a prequel to this series and is a great game if you can get your hands on it)

13)Valkyrie Profile 2

14)God of War 1 & 2

15)Tales of theAbyss

16)Star Ocean : Till the end of time

17)Rogue Galaxy

18.Xenosaga series (if you have a lot of time on your hands, or dont mind unnecessarily long cutscenes, this series can be pretty satisfying

19)Suikoden III

20) Kingdom hearts series.

Just as a personal preferrance, i would stay away from the Grand theft auto series as they are nothing more than overhyped.(im sure this will cause a riot but who cares, they are terrible)

final fantasy 10 and 12

rogue galaxy

tekken 5

soul calibur 3

jak series

metal gear solid series

ratchet and clank series

resident evil 4

suikoden 5

gran turismo 4

need for speed underground 2

star ocean til the end of time

kill zone

devil may cry series

okami

god of war 1 and 2 

1- Metal Gear Solid 3: Subsistence

2- Metal Gear Solid 2: Substance

3- God of War

4- God of War 2

5- Shadow Hearts

6- Shadow Hearts 2: Covenant

7- Okami

8- Shadow of the Colossus

9- Devil May Cry 3: Special Edition

10- Grand Theft Auto: San Andreas

11- Kingdom Hearts

12- Kingdom Hearts 2 

13- Shinobido ( or Tenchu: Wrath of Heaven, but it has 3 more games, 2 of them on ps1 )

14- Final Fantasy X

15- Final Fantasy XII

16- Disgaea ( the best and the deepest strategy rpg, till Soul Nomad is released )

17- Suikoden 3

18- Tekken 5 ( the best fighting game, if you dont like it lets add Need for Speed: Most Wanted as racing game )

19- Shin Megami Tensei: Nocturne ( or Shin Megami Tensei: Digital Devil Saga 1 and 2, these make the list 20 ) 

20- Resident Evil 4

most of these are rpg games. if you want some racing games, i would say Need for Speed: Most Wanted

if you will play with other people, Burnout 2 or Burnout 3's Takedown races ( 2 is more fun than 3 in racing, 3 is just graphical garbage in my opinion ) 

if you like to add another fighting game i would say Def Jam Fight For NY, which is great and maybe better than Tekken 5 in some parts.

if you like more action adventure, you may add Onimusha series ( 4 games or just 1,3 ). 

RPGs

Tales of the abyss

Shin Megami tensei Nocturne (if you can find it) (VERY hard)

Final Fantasy X

Dark cloud 2 (Dark chronnicle if you live in Europe)

Star Ocean:Till the end of time

Xenosaga 1-3 if you dont mind the long-ass cutscenes

Valkyrie Profile 2 (hard)

Shadow hearts series

Action/Adventure

Devil May cry 5th anniversary collection (the 3 games for $30) (hard)

Okami

God hand (hard)

Bully

Grand theft auto (i dont really like it but a lot of people do)

FPS

Time splitters 2/FP (i prefer 2)

Plataformers

Jak series

Ratchet and clank (plataformers/third person shooters)

Fighting

Soul calibur 2

Guilty gear

Virtyua fighter (i dont really like it but a lot of people do)

Marvel vs capcom 2

Rythm

Beatmani IIDX Red (Japan only) (VERY hard)

Beatmani IIDX 3rd ****japan only) (VERY hard)

???

We love katamari

Yeah I know there are more than 20 but you'll probaly

cant find Marvel vs capcom, shin megami tensei, and wont want to import Beatmania.

In no particular order

.hack//G.U. (1 and 2, also vol 3 when it comes out)
Disgaea 1 and 2
Final Fantasy X
Grandia II and III
Shin Megami Tensei (any)
Soul Calibur II
DragonBall Z: Budoaki Tenkaichi 2
Beyond Good & Evil
Prince of Persia 1-3
Xenosaga 1-3
Twisted Metal: Black

1. god of war

2. shadow of the colossus

3. kingdom hearts 1

4. Kingdom hearts 2

5. Resident evil 4

6.  Grandia 2

7. Metal gear 2

8. Metal gear 3

9.  Timesplitters 3

10. final fantasyXll

11. Dragon quest Vlll

12. Guitar hero 1

13. Guitar hero 2

14. Prince of persia

15. Dark cloud 2 

16. Tony hawk 3

17. Xenosaga 1

 In absolutely no order:

1.) Grand Theft Auto 3

2.) Grand Theft Auto Vice City

3.) Grand Theft Auto San Andreas

4.) Tony Hawk's Pro Skater 3

5.) Metal Gear Solid 2: Sons of Liberty(MGS2:Substance if you can find it)

6.) Baldur's Gate Dark Alliance

7.) NCAA Football Series

8.) Madden NFL Series(Sadly)

9.) Max Payne

10.) MVP Baseball MLB series

11.) Time Splitters 2

12.) Blood Omen 2

13.) Twisted Metal Black so freaking unacknowledged....

14.) God of War

15.) Jak II

16.) Medal of Honor: Frontline

17.) Metal Gear Solid 3

18.) Guitar Hero

19.) Escape From Monkey Island (rare)

20.) ESPN NFL 2k5

Hmm...okay, in no particular order other than the random order in which they popped into my mind:

1. Guitar Hero

2. Guitar Hero 2 

3. Resident Evil 4

4. Final Fantasy XII

5. Final Fantasy X

6. Final Fantasy X-2

7. Kingdom Hearts

8. Kingdom Hearts 2

9-11. Xenosaga (all three episodes)

12. Fatal Frame 2

13. Devil May Cry 

14. Devil May Cry 3

15. Need for Speed: Most Wanted

16. Disgaea: Hour of Darkness

17. Atelier Iris: Eternal Mana

18. God of War (haven't played it yet, but heard good things)

19. God of War 2 (same)

20. Rogue Galaxy

wow u must be loaded. 20 of the best games for the PS2 would easily go over $200. well here we go

God of war

God of war 2

naruto choronicles 

reisident evil 4

okami

Final Fantasy 10

Final Fantasy 10-2

Final Fantasy 12

Metal Gear Solid 2

Metal Gear Solid 3(buy substence)

Bully

racing nothing beats gran turismo 4 

Kingdom Hearts

Kingdom Hearts 2

and all kines of JRPG's 

thats all the games to get 

jericoY2J

What he said.

My list:

Not in order tho.

1. Resident Evil 4

2. God of War 1 and 2

3. Final Fantasy X and X-2

4. Final Fantasy XII

5. Devil May Cry 3

6. Grand theft auto San Andreas.

7. Prince of Persia, any of them :P

8. Def jam fight for NY

9. Hitman Blood money

10. Okami

11. Metal gear Solid series

12. Star Ocean till the end of time

13. Tenchu ( I guess....)

14. Bully  

Well Uuuuh.... Thats like all games i know thats worth buying. Of course, if you live in japan/us there is some other great rpgs which isnt in europe /cry like Persona and those

1) GTA 3

2) Final Fantasy X

3) 24

4) GTA vice City

5) GTA san andreas

6) Simpsons Hit and Run

7) Rainbow six 3

8) God of War

9) Burnout 3

10) Final Fantasy X2

i no you asked for 20 but i could only think of 10

In no particular order, just numbered them so that it's 20 games.

1. FFX - great rpg

2. Devil May Cry (the first one) - best DMC game

3. Burnout 3 - fast arcade racer

4. Need For Speed (most wanted or Carbon) - more realistic racer, but not a boring sim like Gran Turismo

5. Prince of Perisa  - great adventure game

6. God of War - good adventure game

7. Sly Cooper or replace with Jak and Daxter - best platform games

8. Maximo or Maximo 2 - great mix of platforming and hack n' slash

9. Viewtiful Joe - same as Maximo but platforming with beat'em up

10. Rogue Galaxy - nice action rpg

11. Timesplitters 2 - the best PS2 FPS because it's plain fun. (bonus co-op play, versus battles)

12.Dynasty Warriors 5 - something for mindless hack n'slash (co-op play)

13. Resident Evil 4

14. Okami

15. Onimusha 1,2, or 4 - one of the best PS2 action series

16. 007 Everything or Nothing - great shooter, fast paced (bonus: co-op stages)

17. Ratchet and Clank 2  or 3

18. Grand Theft Auto 3

19. Soul Calibur 2 or 3 -

20. katamari or a puzzle game like lumines

I have to say this - only fans of japanese rpgs or anime will like Grandia 2, .hack, or xenosaga, FFX-2. Those are not games that everyone would enjoy and I can't fathom including .hack or xenosaga in a top 50 list, let alone a top 20.