Jedi can wear armor, but rarely do. Their fighting style is focused on speed and mobility, and armor tends to slow down a warrior. Armor also isn't all that effective against blaster fire and completely useless against lightsabers, so that to a Jedi would not gain all that much protection either - blocking and deflecting with a saber is far more effective. The Republic also has not been in a real war for a thousand years, and neither have the Jedi. They have adopted the role of negotiators and enforces, but they are no longer soldiers. Soldiers that wear armor, peacekeepers do not. And even the soldiers only down their armor in times of war, and there haven't been a real one in a very long time.

The Clone Wars has changed the equation. The Jedi are at the forefront of one of the greatest conflicts the Galaxy has ever seen. The enemy is numerous, their weapons advanced. The battlefield holds many dangers besides blasters and lightsabers, dangers against which armor protects very well. So more an more Jedi are taking to wearing armor, often armor adapted from Clone Trooper armor. Historically Jedi Guardians have worn armor in times of war, mostly for the same reason they are now taking to wearing it again - protection from the many dangers of the battlefield. Not all Jedi are inclined to wear battle armor - there are many old-school Masters that frown opon its use, for example.