Well, there were two stages; getting the interview and getting in.
For getting the interview, I think my personal statement and letters of recommendation were the key things that got me in. But, the personal statement discussed a lot of my research experience, so I guess having that experience would be the third thing. I had a professors at a couple of universities mention my letters, so that's why I believe those had an impact. Honestly, I think contacting professors only helped in the sense that I didn't waste any applications and apply to places that definitely wouldn't accept me.
Also, I was on the admissions committee for my clinical program this past year, and Statement and LOR were weighted most heavily, after checking off that grades and GRE were good enough.
Interview: I do think it's a bit of luck. I think being prepared to discuss what research/clinical work you've done, why you want to go to X school, how your interests match, etc, is the basis. And honestly, I think being friendly and warm to people(potential advisor, faculty and students) is honestly one of the biggest parts. I ended up talking a lot with two of my advisor's students, not just about the lab, but about tv, movies, etc, and I think that definitely made a difference. They told me that they told our advisor that I was their favorite. I mean, labs certainly vary, but my advisor wants people that are going to get along and that he gets along with. He asks our input every year about who our favorites were for his lab.
So, for interview: my experience with my advisor, and again, as part of the admissions committee is that people look for a combo of experience, interest in mentor/university, and personality.