Okay to start this blog off, these are just theories. Don't be upset if you see the characters as "normal". It's all just a matter of opinion.
With that out of the way, since people seem to hate long blogs, I'm going to keep this brief and to the point.
Twilight Sparkle: She might have a severe case of OCD. What is my argument? She always needs order in her life even checking a checklist multiple times to the point of obsession. For example, in Lesson Zero, she nearly has a meltdown over not being able to mail a friendship letter to Celestia or even the very notion of being tardy. And just the fact that she'd make her friends fight over a toy she played with when she was a filly just makes you wonder just how sane she really is. Pretty easy to see why she might have OCD here.
Fluttershy: She might have (admittedly well managed) anger issues and a case of Asperger's Syndrome/Autism. My argument? Fluttershy has a freaky knowledge of fashion to the point of pointing out all of the flaws in Rarity's gala dress that was made for her. Many people with Autism or Asperger's Syndrome are very good with animals, which Fluttershy fits to a tee. As for the anger issues, she gets mad when she gets rejected by anything, has some issues with patience (though not to the extent of Rainbow Dash) and takes assertiveness training way too far. You want to cheer her on for pushing away the ponies who made her life so difficult but you also want her to calm down and think rationally so she won't ruin the few friendships she's made.
Rainbow Dash: I think she might have ADHD mixed with Asperger's Syndrome/Autism with some anger issues thrown in. My reasoning is that Rainbow Dash has a lack of patience. She likes everything to be completed instantaneously which is probably why Tank is a perfect foil for her. In Testing, Testing 1, 2, 3, she has trouble focusing which is a problem many children or even adults with ADD have. But in addition she's hyperactive and is very rarely sitting down quietly. Up until Read It and Weep, she never really focused on anything besides being the best and has many moments of brilliance and above average intelligence. She just doesn't learn the way other ponies do. She also has anger issues because she tells brutal honestly and speaks her mind, even if it's necessarily inappropriate. Like Sheldon from The Big Bang Theory, another character that's presumed to have Autism, she has moments of insensitivity but can be a really nice mare when she needs to be.
And those are my theories. What do you guys think? Sorry that I don't have an extensive vocabulary like a few users here. Talk about these theories in the comments, but no being offensive. Feel free to talk about alternative theories as well.