As others have pointed out (in a large number of threads), sitting in an hour long queue to pop into a run that has 2/3 bosses down so that you can then re-queue for another hour long wait in the hopes that your "priority" gets you into a fresh run is more than a little off-putting. I know that it doesn't make me very happy, especially when I get into another partially completed run and have to repeat the process, since I need something off of the first or second boss.
So, instead of just complaining about it, I'm going to offer a constructive suggestion that I feel is a good compromise between what we now have and what a lot of (mostly DPS players, due to the long queue times) players seem to want.
Is it possible, and I'm fairly sure that with some creative coding on Blizz's part it is, to implement a system that allows for priority queuing on top of priority for a fresh run? For example, I queue up and wait my hour (yes, it is usually an hour, give or take 15 minutes, on my server for dps without a tank or healer with them) to find myself in a partially completed run and I stick with the group to down the last boss. I would then get priority for a fresh run, as is the current system (even though is does seem to be missing the mark by a large margin since the release of ToT), and I would get placed close to the front of the overall queue for my role (behind others that were in the same situation, of course), behind the people that had already been waiting in queue more than a half an hour or so.
This would help to prevent people from having to sit in hour long queues multiple times for the same raid segment so that they can get a shot at the loot from the first boss or two of the instance. It would, potentially, make the initial queue a bit longer but I think that would be a fair trade for not having to sit in queue for another hour (or possibly two or three) to get into a second or third group.
Of course, there would have to be additional coding put in to verify that the people had not already downed every boss in the raid segment that week, to prevent people that were re-running the raid over and over for Valor (or whatever reason) from constantly bumping those that had not yet run it that week back in the queue. Which would prevent abuse of the system.