It's generally encouraged that players only play through them once... And you can only take a character through any given adventure one time. But, there's not really anything stopping you from doing so (nor is there any real way to track this, shy of you being someone we recognize and remember at conventions or something). Really, you're only robbing yourself of the fun, I think...
But, that said... It happens. Heck, I played through 03-00 three times with Rush, my Missions Street Sammy, and 03-01 twice.
The first time for each was at Origins 2008, the remaining times were in a home Missions campaign, so it wasn't really that big a deal. I just didn't get anything for doing the missions again (No money, karma, etc), and since I knew the plot, I mostly stood back and let the other players make the decisions (Not hard to do, Rush isn't exactly a social butterfly). SO I didn't ruin the game. We just tagged along as we were trying to get a campaign going with some local friends, and they wanted to catch up on the early Missions we'd played already.
Anyway, to answer the original question...
Why play Missions?If you attend conventions or have a local game store that is being used as a Firebase by a member of the Demo Team, it's a way to play an ongoing SHaodwrun Campaign at these venues. Usually convention games are One Shots, and characters are provided, or you can bring your own character, but they don't really "count". Missions gives you a way to create a character and take him from event to event, with different GMs and different players, while playing in the same campaign.
If you don't do the Con scene, you can still use Missions at home. In which case, they're simply short and cheap ready to run adventures, either on their own, as part of a larger Missions Campaign, or even just doing what I often do with official published adventures and cannibalizing them and redoing them into your own unique adventure. In this case, they serve much the same function as any of the old FASA published adventures, or even the newer adventures like the Artifact series.
Bull