I like this one.
Star Trek (Especially the Last Unicorn Games version) and Star Wars (West End Games's D6, 2nd Edition) are by far the two games I find easiest to run.
The reasons for this are manifold, but some of the key elements include:
First, and foremost, I have a love and preference for Science-Fiction gaming, and Space Adventure style stories. I especially love exploration oriented games, which is why Star Trek beats out Star Wars a bit.
The episodic nature of Star Trek, and Star Wars lend themselves to well paced 'world' building as you add new planets, species, and other things each session. Eventually, I can create a unique, personal version of these two well-known IPs over the course of a campaign that feels special to my players, as well as myself. It's not just the Star Trek, or Star Wars universe, but our Star Trek, or Star Wars universe.
My familiarity with the established settings, the tones, and the styles used to tell game appropriate stories in these settings is also a major boon. I never require my players to have a deep familiarity with these universes, but I feel that having one myself helps me make them seem more 'real' when I GM.
That said, a passing familiarity helps a lot, and these are the two most universally well known Space Adventure properties in the history of geekdom. Its extremely easy to run a game in which the players are Starfleet Officers pinned down by Klingon disruptor fire on an ice planet when you don't have to explain what Klingons are, why they might be shooting, and what an ice planet looks like. Sure, you want to describe the features that make this ice planet unique, but the popularity of the setting makes your overall attempt to paint the picture much less stressful.
Both the aforementioned games feature fairly simple systems, without too much crunch, or at the very least they can be run with the crunch turned down a bit. That's important to me, as I prefer the rules of a game to fade into the background as much as possible.
While I can run either Star Trek, or Star Wars with minimal prep (virtually none for Star Wars actually), these are games in which I very much enjoy the prep work.
Other games I find easy are...
Mutants and Masterminds, 3rd Edition
A campaign set in the Silver/Bronze Age DC Comics universe.
Teenagers from Outer Space. I don't even need the book to run it. I can do it from memory.
Faery's Tale Deluxe. It's a simple, rules-lite game, and I'm well versed on the subject matter.
So in conclusion, rules-lite, low crunch games that revolve around specific genres, or properties are among my favorites, and the easiest to run for yours truly.