I am applying to a few programs where the faculty aren't as established (not their fault, just being younger/having less experience). In fact, probably my top choice actually was a graduate student at ASU under the professor I have been working with for the past one to two years. Really, the weakest part of my application are my GRE scores (not that they're weak, just not as strong). I'm also fairly lucky because my advisor at ASU knows a lot of the well known people I'm applying to, I think.
I also forgot to mention that in addition to my thesis in undergrad, I continued working on refininig it with my undergrad professor and we just sent it off for publication to PAID (Personality/Individual Differences) journal. He stated it could be 4-7 months until it is published, because the process can be long and generally takes a revision and resubmit. But, it is something to look forward to!
I would say I have strong to really strong letters of rec, and my personal statement is pretty strong right now (I have been working on it for several months already).