Thought I'd throw this up here as a resource. I haven't really run across the info anywhere else on the web.
The three trails that I know of are as follows:
1)The Westside trail, which takes off from the uphill end of the tunnel on Rocky Butte Rd. Basically as soon as you get out of the tunnel, you hop the guardrail on the right shoulder, a few barely runnable switchbacks and about 1/4 mile later, youre at the bottom of the retaining wall for the loop road at the top. You can go about 200' to the left and up the rail-road tie stairs, or about 10' to the right and up a short but steep slope. From my house via this route its almost dead-on a mile to the top(with a 400' elevation gain), and I've never managed to break under 8 minutes on it. Its brutal.
2)The Eastside trail, through the state park. This one is a little tricky to find because there are a bunch of little paths out to the top of several rock climbing walls...do not sprint down a random path your first (or tenth) time there. The runnable trail is the one furthest to the south. Coming down from the top of the butte there'll be a guardrail on your right, as you get close to the dome buildings at City Bible College and the guardrail stops, hang a 180 to your right (or like a 170 if you want to get all technical about it). The trail heads southward down the slope, then cuts towards the north at the bottom and spits you out on the road just east of the Grotto. For the adventurous there are a few scramble-able routes from the bottom of the cliff back up. Yes, a couple people have died falling of the cliffs recently, yes, there is occasionally an abundance of garbage and bums wandering about, BUT...its one of the more random little trails you'll ever find, and I quite like it.
3)The Northside trail, from the top loop down to the Bible College. This one is damn hard to find...I still have trouble finding it from the top, but its generally in the NW corner of the loop road, looks the most like an established trail vs. the other various little goat trails in that vicinity, and does a couple zigs and zags before meandering down through lush foliage, and a little meadow that I just may be imagining, down to its base near the beach volleyball court at the Bible College. The whole College property is allegedly private property, so I'd peer around for security guards before running out of the forest onto the nice lawn looking all muddy and crazy, you might get tazed. But probably not.
If anyone knows of any other routes on the Butte, I would be super excited to hear about them!
