What I want in a roleplay is so hard to summarize, because the things that I like are so wide and varied. The biggest thing is that I want good characters that fit the roles that are necessary for the story to follow. As for actual stories, I like a wide variety of genres, but I need a romantic subplot.
What I want the most in an rp right now is to have a partner that is creative, inspired, and into the same general things as me to start with one story and then follow into multiple alternative universes with these characters, but I've been looking for that for about 3 years since my last partner vanished, so I'm sticking with looking for someone that can write each role to the story I'm craving any given day.
Things that I could improve upon are vast and varied, but most of them are down to miscommunication as has been hashed and rehashed a few times before.
Lastly, and this is my third attempt at articulating what is the most important to me. In a word, it is the characters.
All of my favorite roleplays have had one theme in common: they had amazing characters that were three dimensional with real reactions to various situations. Whether it was a simple slice of life story with young people that were just living their lives or action/adventure tales of men and women fighting to survive. These were beautifully written characters with flaws and faults and virtues and humor. They had crutches and bad habits and made mistakes, fought over stupid things and made up on a lark. They didn't always stick to the script that I wanted to play with the plot, but they brought life and light to the roles that they were in and I loved these stories the most.
Second most important item is humor. I'm not an overly serious person. The last time I was in a car accident, I made certain everyone else was okay and then started cracking jokes. It's just the sort of person I am and while I know not everyone is, I find that humor makes me like a roleplay a heck of a lot more than something serious.