OK. Let me start off by saying Rammus isn't broken in the typical sense (although late game his dmg is OK combined with the near-perma taunt/knock up), but he is IMO the most broken from a fun perspective. Also, you can slightly break the game (more on that later). Thwarting a Corki Backdoor
Now that I have your attention:
Runes/Summoners The runes are fairly obvious; Domination with Predator, the middle two don't matter and then Relentless Hunter in the last row. For secondary runes go into the Sorcery tree and grab Celerity and Waterwalking. If you don't pop it early, Predator has an almost 100% uptime in URF, so you can literally spam it. For summoners I always go flash/ghost. You could swap flash for something else if you want but ghost is mandatory. In URF, ghost's CD is I believe around double Predator's, and it's the only thing that doesn't have a nearly a 100% uptime.
The Build In order of building:
Predator Swifties (you could go mobis for a higher max speed but I prefer the consistency of swifties)
Righteous Glory - Pretty obvious, more zoom. Helps to achieve max speed if running someone down.
Deadman's Plate - Also more zoom.
Spellbinder - Gives both passive and active movespeed, stacks very fast in URF.
Raptor's Cloak - Speeds you up while running towards turrets.
and Lastly, Youmuu's - Another movespeed active to help achieve mach speed.
With these runes and builds you can reach 6000ms, which is enough for LoL to not accurately keep track of where you are, allowing you to go through people without popping your Q, as shown below:
0.25x Speed so you can actually see it
Full Speed, unfortunately the in-game recorder didn't handle it too well
Enjoy.
