What causes a 1995 Honda Shadow VLX 600 to die when going from idle to acceleration?

There may be several causes, but apart from a fault in the ignition system a vacuum leak could be one of them. These leaks often start out small but then become worse due to the factors of heat and pressure in engine. A leak in the fuel system's vacuum will result in the wrong air to fuel mixture that enters the engine with the result that there is a hesitation in the engine's response to increased fuel or in worse cases a total stalling of the engine. Clean out the carburetors and replace eventual bad rubber connectors from the air filter to the carburetors. Parts inside the carburetor and gaskets may also have gone bad.