How can I keep my chain from falling off the inner chainring? (specifically, from getting stuck in the bottom bracket) I've got a mountain bike which occasionally drops the chain off the lowest gear, and then the chain gets stuck in the bottom bracket.  This happens while pedalling.

Once the chain is there, it takes either a lot of pulling (potentially bending the chain), or removing the crank to get the chain out.

Either way, it's a pain when it happens on the trail.

Note: I'm not talking about chain suck.

And I've seen products like the Deda dog fang chain watcher and Jump Stop, anyone have any experience with these?
There is a bottom limiter screw on the front derailleur which may be of some help. Tension it up till it just goes far enough to shift. It's also possible that your rear derailleur isn't taking up the chain slack properly and is letting it bounce as you go over bumps. This would cause the bottom of the chain to slap as it goes forward to the front ring and could cause it to come off. In that case you might see about replacing the rear derailleur with one on which the tension springs are newer and reduce the slap.