I've had a lot of success with gaming under Wine, but I'm well aware of its limitations and what to expect from it.
In general, if a game supports Windows XP (and thus requires no higher than d3dx9), is not an EA title, is not labelled "Games for Windows" (significantly reducing the chances of using one of the .NET frameworks for anything significant) and has no unusual DRM (ie. uses Steam or has no DRM at all), chances are very high that the game will at least run. If a game is highly popular and meets these requirements (eg. Blizzard titles), you can expect the Wine devs to give it even more attention than usual.
As such, I knew without trying that Bioshock Infinite would not work right away with Wine, and probably won't work for years. Newer EA titles have a higher chance of being problematic in my experience - even without Origin issues, and since the game states Vista as the minimum supported OS, it's reasonable to assume DirectX 10 is necessary (which I think is still mostly just stubs in Wine).
On the other hand, I brought Dead Island Riptide when it came out last week before there were any confirmations on the Wine AppDB that it would run (in fact, there still are none listed - the AppDB maintainers are typically slow to accept new entries), and I just completed the game early this morning. It ran almost flawlessly. "Almost" only because I had to manually kill the process after exiting the game - a very minor inconvenience in my opinion. No hacks, cracks, special DLL overrides, registry edits or anything special required, which is fortunately quite normal these days.
Michael, you mentioned a while back that you were going to report on the lack of DirectX improvements in Wine due to one of the devs possibly having left CodeWeavers or something. Is this still on your agenda?