I have had good success with Round-Up. As someone mentioned there are different kinds of Round-Up available - weed killer and brush cutter - I think. Round-Up, both kinds, are expensive so I have tried other brands that claimed to be "just as good as Round-Up for killing weeds" - they weren't. For weed killing & "edging", along driveways and flowerbeds, I have yet to find anything better than Round-Up around here. IMHO, it's worth the extra $$$.
For the brush killing stuff, wild grape vines, poison oak & ivy, briars, etc. I have found the Bayer brush-B-gone, I think that's what it is called, to be just as good as the Round-Up brush killer. The Bayer stuff is not as concentrated so you have to buy more as compared to the Round-Up brush killer. This makes it slightly less expensive, maybe a dollar or two less per gallon. I have had great results with it though. I keep a quart bottle sprayer, like used to spray/mist flowers, for special occassion with a half-and-half mixture of the brush-b-gone. When I find a large poison oak or wild grape vine, I cut about 6" out and spray both ends. Within no time, maybe a week, it's dead.