Dave was totally right in his VC Monday Madness video: I enjoy Double Dragon glitches. The best-known glitch -- and the most useful -- is the experience factory found in the second level. It's easy to completely fill up your heart gauge and unlock every move simply by walking over to the pile of girders after the climbing fence, then going back across the fence, and back again. This will cause the Williams enemy who was standing in front of the girders to disappear, and you can punch the crap out of his ghost for as long as your timer allows. Later in the same level you can defeat the boss by running away from him. He disappears and the game counts it as victory. I'm also a fan of the glitch-bat, which occurs when you swing a weapon just as it's supposed to disappear, leaving a weird bar made up of other graphical elements from the game.
But my favorite glitch in Double Dragon on the NES is at best useless and actually pretty likely to hurt you. At the end of the first area, you can climb up these -- gutters? Pipes? I don't know what they are. Really, they're just wall decoration. But you can walk straight up that wall. Walk up high enough and you'll come back up to the bottom of the screen. Walk downward and you'll die. Move left and you'll warp back to the ground. Try to jump or attack and you'll fall over. Sometimes one of the Linda enemies will try to follow you up the wall and will just end up in some flickery jiggle maneuver just off the ground.
I pretty much can't get to this part of the game without messing with the wall for a while. I can't even explain why it's so amusing. I could only find one video of this glitch in action (at around 2:50), but be warned -- it's one of those YouTube videos with audio of some guy mocking the game as he plays -- the scourge of the retrogaming blogger.