I can't vouch for the codes here as I don't have a PlayStation. Just because you can't get them to work doesn't mean they are wrong - lots of people say that they can't get the PC codes to work but they work everytime for me.

I presume (2) means twice any PlayStation types care to verify this?

Racetrack Key Code
Did you know there is a racetrack in Lara's mansion?
While in the mansion, press , R2, L2(3), R2, L2(6), R2, L2(5), R2, L2(2).  Check lauras inventory, there should be a race track key there.  If you dont know where the race track is, its where the old maze used to be, and there is a lock you have to use right by the door.  Have fun! Hot4Honda@aol.com

Quad Bike Key Cheats
FROM GROUNDS
Go outside to the corner of the house nearest the Racetrack gate. Line up at 45 degrees . Then use the Alt + Ctrl keys to make Lara jump. Her arm will appear to go into the wall and she will suddenly jump very high and land on the roof (usually after only a couple of jumps if you have lined up right). Facing the way you have landed do a standing jump forward and you should land on the hedge. If you don't land on the hedge the fall will kill Lara.

FROM ASSAULT COURSE
Visit the outdoor assault course and go to the point where you're about to ride on the zip line. But don't get on it! Instead, walk to the top right corner of the square you are standing in (assuming you are facing toward the shooting range.)
Position yourself so that you are standing diagonally facing the perimeter wall. Get as close to the corner as you can then jump straight up and press the ACTION button. Do this until Lara leaps HIGH into the air and winds up very high over the course. Don't run around.
Now face the red square that's floating in the air and WALK to the edge. Move Lara so she is directly facing the red square and do a regular STANDING JUMP. When on the red square, move so that she is facing the opposite way that she was facing when you were in front of the zip line. Now walk to the corner facing the back of the course.
Press back once then run and jump. If done correctly you should be on the roof. From the roof you can jump onto the hedge surrounding the area where the quad bike is. Then jump into the Racetrack - NO KEY REQUIRED!
morehtml@hotmail.com
I got a time of 43.30secs I found a little area that you can take a short cut with hehe I've got screenshots of most of it and will have it up tomorrow.

Flying Code
A demo of TR3 was given out by pizza hut. On the demo i found a very
strange thing.  if u hold L1+ L2+square and X  lara will be able to swim in
air.  i have tried to do it for the real game but have been unsuccesful as
of yet. jheller@southwind net

Level Skip Code
While playing a game, quickly press L2, R2, L2(2), R2, L2, R2, L2, R2, L2(4), R2, L2, R2(4), L2. If you've got it right, Lara will say "Nope".

All Guns and Full Ammo Code
While playing a game, quickly press L2, R2(2), L2(4), R2, L2, R2(2), L2, R2(2), L2(2), R2, L2(2), R2. If you've got it right, Lara will scream.

All Secrets
While playing a game, quickly press L2(5), R2, L2(3), R2, L2, R2, L2(2), R2, L2(2), R2, L2(2). If you've got it right, Lara will say "Ahhhh". The "All Hallows" bonus level becomes available if you use this code.

Full Health
While playing a game, quickly press R2(2), L2, R2, L2(6), R2, L2(3), R2, L2(5). If you've got it right, Lara will say "Ahhhh".

Other Codes
If anyone knows any other tricks or cheats email me on nfreeney@ibl.bm and I will include them with a credit.