Pretty much anything by Blaise Russel and Ransom Arceihn is good. If you have an up-to-date system you should probably try and get FS2_Open working, things will at least look much better and a number of the good campaigns actually require it.
Anyway, large/notable campaigns (ie mostly my favorites):
Derelict
The Aeos Affair
Sync
Transcendant
Homesick
Shrouding the Light
Inferno (Don't let me catch you pimping it as FS3 though)
Dishonorable mention:
The Second Great War Part 2, if I'm remembering that right. The sheer crapiness of this campaign makes it worth playing at least a few missions. Basically the mission designer didn't bother to name ships, threw in a bunch of Colossuses and Sathanii, and had some subplot about the commander of the GTVA military handing his post over to one of Bosch's Lieutenants so that he could look at a Sathanas that he stole.