Cardinal Spear - A good campaign, though too easy. Except the last mission...
FSPort - Original Freespace brought to FS2. Still very enjoyable today.
Operation Templar - Fun canon multiplayer mini-campaign turned single player. Play FSPort and Silent Threat Reborn first.
Silent Threat: Reborn - Exceptional. But play FSPort first!
Awakenings - This is a very good campaign.
Operation: Crucible - Supposedly the only fully branching campaign. And fine work.
Destiny of Peace - I don't remember it well, but I enjoyed it.
Tango - Haven't played. Plan to.
FreeSpace 2 - It's Freespace 2! Play it!

Advise all the FS1 canon stuff first.
Fall of Epsilon Pegasi - I played this I believe on an incompatible version. Could only run a few missions but enjoyed them. I will try again now I have 3.7.0 sometime.
Lightning Marshal - Haven't played.
Pandora's Box - Haven't played.
Titan Rebellion - Haven't played.
Transcend - regarded as a classic around here, I haven't played it yet. I don't know how to find the best working version either, please, do tell if you do, as I want it.
Blue Planet: Age of Aquarius - despite the fact I don't like the player character (some do) this is still a highly polished campaign with an enthralling story. A little light on action, but still highly recommended.
Blue Planet: War in Heaven - haven't played it, but lots of people think it's awesome.
Derelict - Gave up on this after a particularly difficult, lazily, badly FREDded mission. Only campaign to make me do that. However, I have seen it let's played, and it's a vast campaign with otherwise great missions and a great story. Well worth your time, and regarded as one of the classics around here. I will pick it up again eventually.
Aftermath - played this very recently. It's a good campaign.
Warzone - Haven't played.
Phantoms - These two are both good mini-campaigns.
Echo-Gate - recommended this to someone a few days ago.
Advice, play all the canon stuff first. All other campaigns based off the canon will then make so much more sense.
Also, consider my favourite campaign, Wings of Dawn.