Get a decent level Wobbuffet, the ability of which is Shadow Tag which prevents fleeing. Careful with that though, I think the majority of Entei's moves are special and if you use Mirror Coat (which deals back twice the damage taken from any special attack) you have a risk of killing it. Also I think Diglett/Dugtrio can have the ability Arena Trap, which prevents fleeing and I'm fairly sure they can learn False Swipe by leveling or through TM use.
Alternatively you could get a Smeargle and get it to learn Mean Look/Spider Web and False Swipe, the downside to that is that Smeargle are usually quite weak unless it is a ridiculously high level.
Greeboz said:
To everyone telling him to use a move that stops Entei from running away: DON'T! If he uses Roar when he can't run on his own(After a Mean Eye or Spider Web) He will be gone forever. I doubt they changed that from the 2nd Gen.
One solution to that might be getting Smeargle to learn Ingrain, which negates the effect of Roar (and also restores a bit of HP per turn). However I'm not entirely sure on that so don't quote me on it.