What's the shortest / easiest "granny gear" available?

Gearing is commonly described in Gear Inches and to clarify, having your chain in the smallest front ring and the biggest rear cog results in the smallest gear.

Chainrings

The smallest chainring I've seen on a 5-arm crankset is a 20T, although 24T is a lot more common.

8-Speed cassettes

Shimano had a line called "Megarange" that was 11-34T. I believe it's no longer manufactured but you can find them online sometimes.

SRAM has a cassette in the PG-850 line that is 11-32T that I believe is still available.

9-Speed cassettes

Shimano has a number of models that are 11-34T and one model that is 12-36T.

10-Speed Cassettes

I believe the biggest you can get is 12-27T.

IMPORTANT NOTE: Not all front or especially rear derailleurs will be compatible with these large range rings and cassettes. Check with the manufacturer - most have spec and compatibility docs online.

Out of curiosity I used a gear calculator to figure out what the gear inches would be if you actually configured a bike and could ride 20x36 on 700c wheels...an incredibly small 14.7 inches. That means every pedal revolution you travel about 46 inches, just over half the circumference of the wheel.

My Giant Yukon came with a 22 tooth inner chainring and a 32 tooth cassette although now I have a 34 tooth cassette on there. It is nice for climbing up hills although you can still begin to struggle above 20%. The legs will turn the gear easily enough but you'll still get puffing and panting to maintain a reasonable cadence. You can get these new 40, 42, 50 and 52 tooth cassettes available. I'd love to try 22/52, that would be the rock crawler of bicycles.