You basically need to use a combination of the Steam Trading Card FAQ in conjunction with the Steam Trading Card Community Group announcements. Over time the FAQ will get updated but for completely up to date information you will need to watch out for announcements.
For example, at the time of writing the support games as per the FAQ are as follows;
- Borderlands 2
- CS:GO
- Don't Starve
- Dota 2
- Half-Life 2
- Portal 2
- Team Fortress 2
- Left 4 Dead 2
- Sanctum 2
- Go Home Dinosaurs!
- Triple Town
- Cubemen 2
- Monster Loves You!
- Really Big Sky
- Faerie Solitaire
- BIT.TRIP RUNNER 2
In addition to these, the following games are listed in the Steam Trading Cards group announcements;
- Monaco
- A.R.E.S.
- Trine 2
- They Bleed Pixels
- Defender's Quest: Valley of the Forgotten
- FTL: Faster Than Light
- 1... 2... 3... KICK IT! (Drop That Beat Like an Ugly Baby)
- Strike Suit Infinity
- Zach Zero
- Tower Wars
- Serious Sam 3: BFE
- Anodyne
- Super Meat Boy
- Blocks That Matter
- Brütal Legend
To see a list of games that you own that have badge support, in Steam hover over your name in the Navigation bar and select Badges;