This is something I've been thinking about a fair bit lately, because we are JUST making the transition to cloth from paper around here, and the draining-oily-foods problem has been on my mind. What I've been thinking, and this is tentative, is that we'll use linen napkins when something's supposed to come directly into contact with food. If you're not using linen around the house, you're missing out--strong, durable, absorbent (yes, really, you just have to beat it around for a while first) and non-linty, which last property is particularly relevant here. However, as has been pointed out elsewhere on the boards, clothes dryers and oil/grease don't really mix safely, so I'd probably give the napkin a quick hand-sudsing in the kitchen sink before I threw it in the laundry to get off the worst of the oil.
Also, it's only tangentially connected, but I'm too excited, so I'll tell anyway--I LOVE bacon, and it's always been such a pain to cook, but recently we've just started cooking it in the oven! SOOO much easier. I've found that 400 or so is a good temperature range. Next time I do this, I'm going to see if cooking it on the broiler pan allows it to drain while cooking, and if it does, then I will be in heaven (other than cleaning the broiler pan...though I do save bacon fat, so it's not too bad.) If that works, that should eliminate one of the few things we still regularly use paper towels for.