According to Wine Spectator, wine does not spoil in the same way many foods do, but alcohol poisoning and other unpleasant consequences can occur when one drinks too much wine. Fortified wine, such as Port wine, can be especially risky.
The Wine Spectator explains that wine does not spoil because the alcohol in the beverage acts as a preservative. Wine that is described as having turned bad is typically wine that has not aged well. The source says that bad wine is typically identifiable by a brown color and nutty, instead of fruity, notes in its flavor. Bad wine has no risks associated with it beyond the risks associated with alcohol in general.