Aragorn's most famous weapon is the sword, Anduril. It was passed down to him as part of the heirlooms of the line of Kings. This sword was previously named Narsil, broken when it was used against Sauron in the battle of the Last Alliance. When Sauron showed himself again, reaching out for his Ring and causing the Quest, Narsil was re-forged in the House of Elrond for the King to take into battle, reclaim his throne, and begin the Time of Men.
Galadriel gifted Aragorn with a sheath made to fit Anduril:
"It was overlaid with a tracery of flowers and leaves wrought of silver and gold, and on it were set in elven-runes formed of many gems the name Anduril and the lineage of the sword. 'The blade that is drawn from this sheath shall not be stained or broken even in defeat', she said." -- The Fellowship of the Ring, "Farewell to Lorien"
No other weapons are mentioned for Aragorn, but one might assume that he at least had a knife suitable for an ourdoorsman who hunted for food. He might have preferred not to use it in fighting, but it would have been available at need. He is not said to have used one to help in blocking, or in a knife fight.
In the Peter Jackson movie, a bow is shown in use by Aragorn in Balin's Tomb. In the book, Fellowship of the Ring, "Bridge of Khazad-dum", Aragorn used his sword with no mention of his using a bow. Only Legolas used one in the book scene.
Article written in response to a question from a reader named Chris.