The Orange Box cheats for the Xbox 360

Achievement Hint: Dancing Vortigaunt
You can find the "dancing" vortigaunt in Water Hazard at the part after you take down the chopper. Once you open the gate, look to the opposite side and you will see a pipe. Enter the pipe (which is difficult; try using something to stand on) and follow the passage until you see a friendly Vortigaunt who talks to you.
Achievement Hint: Garden Gnome (Episode 2)
The gnome is in the room in the first chapter where Alyx tries to contact her dad. The gnome should be under the bed on the right hand side of the door you exit through. Don't forget to shut the hatch once you put him in the cannon or the achievement will not register.
Cheat: Free Health

The code scheme popularly known as the Konami Code works during Half-Life 2 Episodes, oddly enough, and will generate a Health Pack for your use. The code can be done over and over again: Up, Up, Down, Down, Left, Right, Left, Right, B, A.

Cheat: Full Ammo

If you're in need of ammunition for your currently-equipped weapon during any Half-Life 2 or Episode 1 or 2, insert the following code to max out your ammunition: Y, B, A, X, Right Bumper, Y, X, A, B, Right Bumper.

Note that you need to re-assign the Gravity Gun button (or clear it completely) or the code will add null ammo to the Gravity Gun.
Cheat: Invincibility

For character invincibility in the Half-Life 2 titles, insert the following code during gameplay: Left Bumper, Up, Right Bumper, Up, Left Bumper, Left Bumper, Up, Right Bumper, Right Bumper, Up.

Cheat: Portal Cheats

Insert the following button commands during gameplay for the desired result...

Create Box

Down, B, A, B, Y, Down, B, A, B, Y

Fire Energy Ball

Up, Y, Y, X, X, A, A, B, B, Up

Fire Rocket Projectile

Up, Y, Y, B, B, A, A, X, X, Up

Portalgun ID 0

Up, Left, Down, Right, Up, Left, Down, Right, Y, Y

Portalgun ID 1

Up, Left, Down, Right, Up, Left, Down, Right, X, X