Note: Remember that level 20 is the last level in Fallout 3. Unlike every other level of Perks, you will only be able to select one Perk from this list. Be careful to choose one that you'll find useful for the rest of the game.
Explorer Requirements: None - This perk reveals every location on the map. This has nothing to do with the power or effectiveness of your character, so the decision to take this is up to you. Would you rather come across locations randomly, or would you like to have them already located on your map, allowing you to explore in a more planned fashion?
Grim Reaper's Spirit Requirements: None- If you kill a target in VATS, you have all of your action points left when you leave VATS. Insanely powerful? Yep. A deadly high-level character never really has to leave VATS once this perk is selected. As long as you're not a melee character, this is the best level 20 perk.
Ninja Requirements: Melee Weapons 80, Sneak 80 - Increases your chance to perform a critical with melee and unarmed attacks by 15%, and sneak attack criticals do 25% more damage. This is a very powerful perk which, when stacked on top of other crit and sneak-attack improving perks, and can turn your melee or unarmed character into a real powerhouse. There is a catch for unarmed characters, however - you need 80 points in melee weapons to get this perk. That is a pretty big catch, and makes this perk a poor choice for unarmed characters. Even if you planned to have the 80 points in melee, those 80 points could go into some other more useful skill.
Solar Powered Requirements: End 7 - With this perk, you gain two points of strength when in sunlight and you regenerate health. If this perk was placed somewhere lower, it wouldn't be terrible. But as a level twenty perk, it is awful. Grim Reaper's Spirit is far, far better in any situation.