Hmm, if you're running a game in the Rebellion era or later, you can do adventures based around trying to recover lost knowledge about the Jedi and the Force. There can be (and probably are) dark siders who are trying to get the same thing at the same time because ADVENTURE!, so you have a Raiders of the Lost Ark kind of situation.
In other eras it's probably not the Jedi who are trying to recover lost knowledge, but the Sith or other dark siders might be trying to recover lost dark side knowledge, and the Jedi need to try and stop them. I've done a couple of different treasure hunt adventures like this.
If you're in the mood for straight up combat, Jedi are uniquely well suited to leading from the front, at least the way I do mass combat. We use squad rules from the Clone Wars CG, combined with the Padawan rule from the Jedi Academy Training Manual, whereby PCs on the battlefield can soak attacks directed at friendly squads within 12 squares of them. Since Jedi can use Deflect to take half damage or no damage from a squad's area effect blaster fire, they can hold up longer while soaking damage for friendly squads, giving those squads greater longevity and combat effectiveness.
At the other end of the spectrum, high ranking Jedi can be deeply involved with politics, and scenarios where they have to build political coalitions, and try to juggle their moral and ethical values with political necessity can do a lot to help define those characters as well as the campaign world itself.