Depends what bike I'm riding. On my road bike the steepest I generally tackle is probably 10%. On the mountain bike 22% is not uncommon. The steepest I climb I can tackle and be pretty certain I won't have to walk is 18%. The thing is, though, the mountain bike has 32 front 51 rear gear. The road bike has 36 front 28 rear.
I live in the Surrey Hills so anywhere I cycle I'm pretty much guaranteed a reasonable bit of climbing somewhere. One of my favourite rides takes me over Box Hill; it's mostly at around 5% with brief bursts up to 8% but it's a good long run of about 15 minutes for me. There are plenty of steeper rides around here but Box Hill gives a good workout and I know that however tired I am I won't have to walk any of it. In fact, now that I'm riding the area regularly, I have to be pretty knackered to even need my lowest gear.