It's a decidedly case-by-case question, and you shouldn't let silly things like "data" and "value judgments" get in the way of an enthusiastic impulse purchase. But for the more prudent types, Consumer Reports has compiled handy a repair-or-replace guide.
The magazine drew together reader survey results with their own internal data to evaluate peoples' experiences repairing and replacing certain classes of products, and the results aren't terribly surprising: Point and shoot cameras are cheap and difficult to repair, and get noticeably more advanced over short periods of time, you may as well just replace them if they break outside of two years of ownership. LCD HDTVs? Hold on a little longer.
Granted, the general trend here seem to be that it's not worth repairing anything that's more than a few years old, so it's less a guide about when to replace than confirmation that today's gadgets—even the most expensive ones—are more or less disposable. Full chart below. (Click to enlarge) [Consumer Reports via Consumerist]