How many games of solitaire are winnable?

Most of them in the easy games, and far from all in the hard ones. FreeCell gives the cleanest count: its first Windows version used a fixed set of 32,000 numbered deals, and volunteers eventually solved every one except deal #11982, so 31,999 are winnable.

Klondike has no fixed deal set, so it is measured as a rate instead: about 90% of turn-1 deals and 82% of turn-3 deals can be won with perfect play. Golf and Pyramid are stingier. In our own run of 500 deals each, 228 Golf games and at least 303 Pyramid games were winnable. Deals are never screened first, so some simply cannot be won.