Not wholly sure if this is appropriate, because I just signed up, but worth a shot anyway.
So, I'm playing in a rather unconventional online game- in that although I'm technically the GM it's equally moderated by other people playing, and most missions and things are collaborative. As in, "Hey, we have these guys- it would be fun to do X with them-" Right now, however, I'm trying to get some ideas generated for mission type things to send the characters on.

Here's an abbreviated rundown of the setting:
Fantasy/medieval level technology, aided in places by magic. The main race being played is Arcanic (made up for this game) which are both like humans and elves, very long lived, most have some magical ability of some kind. To the north and west are human countries (Nempen and Grymme respectively), between them is dwarf and orc country as it's primarily made up of mountain ranges. It should be noted that orcs are equally as civilized as any other race, functioning more as a tribal society rather than just nefarious monstery things. And to the south are elf lands, extending far into the south. Coastline is to the east, mountains to the west of the Arcanic country. the country of Reume, where most of the story takes place is a monarchy. The king is mostly benevolent, but sort of- daffy, for lack of a better term.

These are the people currently involved:
All Player Characters are currently members of a mercenary organization called The Eyrie, that consists of about 1500 people. The head of the Eyrie is a mercenary named Faucon.

Sparky: 30 year old male. Lightning and mind mage with teleportation and location magics. He's not much of a fighter and blood makes him nauseous. A gentle, and old soul. Recently inherited an two estates and a substantial sum of money. Standard member of Legerdemein (Mage Division of the Eyrie).
Raveyne: 35 year old (human equivalent) male. Assassin and woodsman. Very good at climbing and breaking into buildings and living off the land. Strong hand to hand fighter, not as comfortable with weapons. Extremely pragmatic and logical. Married to Sparky. They have a 2-year old (human equivalent) son. Currently the Second in Command of Talon (Assassin and Rogue Division).
Gwydia: 20- year old girl. Primarily a thief, very mouthy, specializes in picking locks and escaping bonds, and trick riding. Excellent with throwing knives and swordfighting. Standard, though spoiled, member of Talon.
Ayen: 30 year old male. Assassin and powerful fire mage. Excellent skills with a sword, also good with throwing knives and daggers. Also has extensive knowledge of history, governement, and etiquette. Currently engaged to Gwydia. They have 4 year old twins. Head of Talon.
Jack: roughly 40 year old male. A pirate, and more recent member of the Eyrie. Hired on to head a new maritime division, called Thessalus. Good at pirating, but gets himself in trouble with his lechery. He and Gwydia have only recently resolved some long standing issues between them.

Anyway- that's who we have. Recently Gwydia and Ayen's babies (the twins) were kidnapped, as was Sparky, so it would be nice not to do another kidnapping mission. But again, any suggestions are appreciated.

Hi, and welcome to the Forge!

I'm a little unclear on what you're asking for, and the type of play you prefer.  When the group is having a good time, what are they enjoying most?  Lots of scheming to get the most advantage out of the system, and show how effective they can be as players?  Or immersing in the society and customs of an exotic world?  Or in telling stories about human values and timeless truths?  Or something else?

If you're looking for ways to generate some ideas for stories, I recommend Chris's blog on Flag Framing and the Conflict Web, which are pretty handy techniques.

Note, by the way, that you don't necessarily need "missions" per se.  You can just create a powder keg, and have the heroes ignite it (intentionally or by accident), and duck as all hell breaks loose and each of the NPC's pursues their own agenda, trying to rope the PC's in.

Mostly I say missions because the Eyrie as an organization is often hired by outside parties, nobility, townships, that kind of thing to accomplish stuff that needs doing. Assassinry, providing extra security, tracking down missing persons. So- the system has a built in 'mission' format, and things just kind of land on the characters' heads.
The majority of play however, has been dealing with relationships between the characters and tensions there. Which generally I find the most entertaining. Probably should have also mentioned that since it's a collaboratively-GM'd game, I also play two characters- Raveyne and Ayen. It's a weird system...
Mostly I'm looking for fairly general things to throw at these guys. A piratey mission would be fun.

I shall point you to The Cheap & Cheesy Adventure Generator, and if you're like me and didn't quite see the best way to use it, Vincent Baker's essay about creating situations.