God Mode
NOTE: ALWAYS MAKE A BACKUP BEFORE CHANGING GAME FILES.
Locate the difficulty files in your Crysis installation folder (ie: C:\Program Files\Electronic Arts\Crytek\Crysis\Game\Config). These files are called diff_easy.cfg, diff_normal.cfg, diff_hard.cfg and diff_bauer.cfg. Open the file (with Notepad) that corresponds to the difficulty level you are playing. Add the following line to the end of the file and save it:

g_godMode = 1

Now, when playing your health will still decrease but you will not die. Instead, your health and armor will automatically replenish when your health reaches 0.

More Cheats
NOTE: ALWAYS MAKE A BACKUP BEFORE CHANGING GAME FILES.
Using the same method as above, add the following lines to the end of your config file for the corresponding effect:

i_unlimitedammo = 1: Unlimited Ammo
ai_IgnorePlayer = 1: Enemies Ignore You
i_noweaponlimit = 1: Carry Unlimited Number of Weapons

You can also modify your suit stats. For example:

g_suitCloakEnergyDrainAdjuster = 0: No energy loss
g_suitRecoilEnergyCost = 0: No energy cost
g_suitSpeedMult = 2.85: Run faster
g_suitArmorHealthValue = 900.0: More armor points
g_playerSuitArmorModeHealthRegenTime = 0: Instant health regen
g_playerSuitArmorModeHealthRegenTimeMoving = 0: Instant health regen while moving
g_playerSuitHealthRegenTime = 0: Set health regen time to 0
g_playerSuitHealthRegenTimeMoving = 0: Set regen time while walking to 0
g_playerSuitEnergyRechargeTime = 0: Set energy regen time to 0
g_playerSuitEnergyRechargeDelay = 0: Do not wait until energy regen starts
g_difficultyLevel = 1: Set difficulty, 1 is easy, 4 is most difficult
After making all of your edits, save the file, load up a new game and see what you've edited!