I agree that pruners or the handsaw is probably as good as a knife if needed in a tree. That being said, IIRC, when I was climbing on a regular basis I carried the K.I.S.S. knife that someone else posted the link to with me. More out of habit that out of necessity. I'd take my wallet and keys out of my pockets because they were uncomfortable while wearing the saddle, but leave the knife. (I'd also take my cell phone and fire department pager too- didn't ever respond to a fire from 50' up though!)
I too can't think of a time when a knife would be needed, however, if you don't have it, some day you will need it! Most likely while on the ground and still in your saddle. A multi-tool is usually a safe bet to carry, I use mine many times per day.
As for the K.I.S.S. knife opening on me, no, I've never had it happen on accident. I've had mine for ~3-4 years and carried it on a daily basis. At times the screw gets a little loose and needs re-tightened though. Mine is always clipped on my pocket with the blade on the inside, so that might help persuade it to stay in. The biggest complaint I have is that it is very hard to get (and keep) a good edge on the straight part of the blade, but the serrations work great for cutting twine, rope, ect. Really makes a bad letter opener too, with only one side of the blade sharpened. It's not a bad knife, but I probably wouldn't buy another one, there are better one's out there.
Dan