Viggo Mortensen apparently really is Aragorn

At least, he's one cool motherfricker...

From the "trivia" on IMDB:

Viggo Mortensen did his own stunts. He also insisted on using only the real steel sword, instead of a significantly lighter aluminum sword, or safer rubber sword, which were manufactured for battle scenes and stunts.

Viggo Mortensen chipped a tooth while filming a fight sequence. He wanted Peter Jackson to superglue it back on, so he could finish his scene, but Jackson took him to the dentist on his lunch break, had it patched up, and returned to the set that afternoon.

Viggo Mortensen (Aragorn), who is trilingual in English, Spanish, and Danish, requested the script be revised, to let Aragorn speak more of his lines in Elvish.

Veteran Sword Master Bob Anderson called Viggo Mortensen "the best swordsman I've ever trained."

Viggo Mortensen purchased Arwen's horse after production and gave it to Liv Tyler's riding double.

Viggo Mortensen kept his sword with him at all times off-set, so that he could remain in character. He was questioned several times by Police, after reviewing his training sessions with the sword, and being spotted by members of the public.

Because Lawrence Makoare's vision was impaired while he was made-up to look like Lurtz, he could not pull punches during the sequences when he battles Aragorn in hand-to-hand combat. Rather than having Makoare do this sequence over until he could pull his punches, Viggo Mortensen decided to fight back just as realistically, making the physical blows completely real.

Viggo Mortensen broke two toes while kicking the steel helmet by the orc pyre, and that take is the one that appears in the final cut. Director Peter Jackson said that he was really impressed with the shout of pain Aragorn cried out for the fate of the two Hobbits, realizing only later that it was real pain for his toes. He was also impressed by the fact that Mortensen continued acting, even while so seriously injured. Mortensen later remarked that the only reason it was even mentioned, on the DVD release, was because he was an actor, and that the stunt crew were injured far worse and pushed through it.

The dawn shot of Aragorn, Gimli, and Legolas pursuing the Uruk-hai, came about when Viggo Mortensen persuaded the Second Unit team to camp-out on-location. Mortensen's efforts in organizing the overnight trip were so effective, that actors and crew from the other film units, including Miranda Otto, came out to join him.

Viggo Mortensen estimates that during the course of filming the trilogy, and including all of takes, he "killed" every stuntman on the production at least fifty times.

Also, one that's not on there...

The scene at the end of Fellowship when the orc throws a knife at Aragorn/Mortensen and he knocks it away with his sword was a sheer accident. The orc was supposed to use a prop/rubber knife and messed up. Mortenson could have been seriously injured but for his quick reflexes.