Home made hamburgers always fall apart on me. Now I just don't even bother and kind of throw it on my plate and eat with a fork. :( I also really hate hate hate the grease just grosses me out.
Next time use ground sirloin.. Very low fat content. I don't have problems with patties falling apart anymore (used to) but the secret (assuming you're grilling) is to form the patties, then stick them in the fridge for a half hour to an hour so they can firm up and oil the grate (after letting it get hot, use a paper towel with some oil on it) right before you put them on. After they're on, leave them, for at least 5 minutes.. Use a spatula carefully on one as a tester, they should have the same rigidity they had when you first took them out the firdge (they shouldn't bend or fold easily) then flip them.
(This isn't directed at you specifically, just a general tip for anyone who likes to grill)
I like to cube up (1/4 inch cubes or so) some cheese and roasted jalapenos in my patties before I cook them.. Make sure the cheese is covered by a layer of meat or it'll just melt and fall out.. Peperjack works well.