Where can I find the strongest armor in Fallout 3?
Everything in Fallout is a trade off. I believe the best armor I got though was the winterized armor found in the Alaska simulation.
Beneath Fort Constantine you can access "Bomb Storage" (using a key from Dukov, Ted Strayer, or any of the others from the "You Gotta' Shoot Em' In The Head" quest) and pick up the T-51b Power Armor - with +50 damage reduction, more than any other armor in the game. The winterized armor mentioned in another answer only has +45 DR.
There's only one of it in the world. I successfully completed the "You Gotta' Shoot Em' In The Head" quest during one character build and upon entering the room found the armor had been taken, so keep that in mind when you play through other quests.
In terms of DR, it's a tie between the T-51b power armor (in Fort Constantine; related quest: You Gotta Shoot 'Em in the Head) and the Enclave Hellfire armor (worn by some Enclave Soldiers and Enclave Hellfire troopers if the Broken Steel DLC is installed). Both have 50 DR and 2000 item HP.
The Hellfire has the same DR as the T-51b power armor and high durability, and boasts the added benefit of +30 Fire resistance and +1 Strength. The only drawback is that the helmet gives a penalty to Charisma, while the T-51b's does the exact opposite.
However, the Hellfire can be repaired with other Hellfire armors, whereas the unique T-51b can only be fixed by merchants. The fact that Enclave troops wearing the Hellfire are somewhat uncommon does reduce the appeal, but that should not discourage.
Note that the armor, as DLC material, cannot be turned in to Casdin for his quest.
Comparison of Fallout 3 power armors
Source: The Vault wiki, Enclave Hellfire armor
The T-51B Winterized Power Armor Earlz was referring to is the strongest armor in the game. You receive it after completing ALL of the Operation Anchorage content. It is located in the armory you are given access to at the end, before leaving the simulation, as is the Chinese Stealth Armor. You want both of these, and you'll want to grab the Gauss Rifle as well, if you've not already gained access to the alien technology via the Mothership Zeta DLC. You will not be able to obtain them at any other point in the game.
The T-51B armor is "broken" in that it, essentially, never takes any damage. Also, the helmet is a stackable item.
If you scroll to the very bottom of the page, in the link below, the first entry in the "Bugs" section explains this fact (which exists in PC, PS3, and XB360 versions).
Winterized T-51b from Operation: Anchorage is the best- it may have less DR than the normal T-51b, but that all changes when you go into combat. The Winterized T-51b never needs to be repaired, while the normal version breaks down alot. Also, its damage resistance is really high.