I've worked up a list of 27 of what I consider Basic or Standard Jedi Missions and Activities. I made this because there aren't any real adventures in the books just for Jedi. These are without any details, but could be used to help write up your own adventures. There is some overlap a bit and the last one is pretty much a given, but I wanted to include it. The term "Crisis Reserve" was used in the novelization for The Phantom Menace, and are Jedi who aren't currently on a Mission, but are ready to go at a moment's notice.
Let me know what you think,
Zenji
Protect Citizens Of The Republic
Secure Galactic Peace And Dispense Justice
Document And Report Hazards, Dangers, and Threats
Advise And Assist Planetary Or Local Security Forces
Protect Or Rescue Important Dignitaries
Gather Evidence Of Criminal Activity
Apprehend And Detain Republic Fugitives
Suppress Insurrection In The Republic
Obstruct Space Piracy Between Worlds
Deter And Hinder Spice Smuggling
Prohibit And Extinguish Slavery
Defend Republic Borders And Repel Invaders
Mediate Negotiations And Disputes
Evaluate And Investigate Disturbances In The Force
Ascertain And Verify Official Or Jedi Misconduct
Capture Or Destroy Dark Side Personages
Recover Artifacts Related To The Force
Safeguard Important Republic Locations
Help Republic Citizens In Need
Standby On Crisis Reserve
Train With A Jedi Master As A Padawan Learner
Build A Lightsaber
Take The Jedi Trials And Become A Jedi Knight
Train A Padawan Learner And Be A Jedi Master
Become a Jedi Council Master
Train Jedi Younglings
Travel Across The Galaxy