What is the problem(s):
1. Slow Cydia download: Downloading the actual Cydia app is slow.
2. Cydia sources are unresponsive or missing: Downloading packages takes forever, and you are missing lots of repos. ModMyI and BigBoss Repos seem to be the most noticeable repos with problems. There may be others. You'll also notice that these two repos may also be missing.
3. It's slow to add sources: This is actually due to the problem directly above, it's not the new repo that's giving you problems, its the ones that are unresponsive since it still tries to download from them too.
4. Cydia not initializing: This is due to either GreenPois0n not being able to fully download Cydia, but still installing it anyways. Thanks to lg12345 and souljaboitellem for information on this.
Explanation of the cause of the problems:
I hate to break it to you, but it's not Cydia. It's also not your iDevice. On top of that, it's also not GreenPois0n... So what is causing the problem?
Simple, the problem is the servers. Each repo is put on a separate server. These are owned an maintained by different people/companies/groups. Since there are a mass amount of people trying to get into Cydia after jailbreaking 4.2.1 with the recent release of GreenPois0n, the servers are getting swamped. This makes them unresponsive and unreachable. Now that you know the problem, I'm going to talk about the only "solutions" (which aren't really solutions).
"Solutions" to the problems:
* There is really no real solution for this. You either have to use the servers when no one else is, or just wait it out.
* Timing: use the servers when no one else is. You'll notice that it is still slow, but you can actually get things done. Many people don't have this option since the time when no one else is using the servers is late at night.
* Wait it out: wait for everything to level out. This can take days to weeks. Everything will eventually fix itself out as less people need to connect to the servers. Patience has brought you this far, use it a little while longer.
* Applies to problem 1 only: Use RedSn0w to install Cydia. Many of the source/repo problems will still be there though. According to lg12345, this can also fix the failure to initialize Cydia problem.