I agree that the best use for miles (for me at least) has been on last minute emergency travel. In general, it seems like many of the majors become a lot more flexible in redemption rules when it's REALLY near flight time. In fact, in my experience, that's where the airlines really shine. Some examples for me have been:

1. Next day trip on Delta from SFO/SJC->Lima, Peru when my girlfriend got sick in Cuzco (would have been about a $2-3K ticket for a walk up fare, cost 35K miles)

2. Same day travel SFO->JFK when (the same) girlfriend's father was diagnosed with a heart problem requiring next-day surgery. (cost for medical emergency fare $800, cost 25K miles)

3. same-day travel SFO->PIT when (the same) girlfriend's sister went into labor and she wanted to be there with her (didn't even bother to price that one, but cost us 25K miles).

4. next-day travel Fresno->IAD when an aunt's sister went into a coma (travel was for the aunt). (best fare we found was $800, cost us 25K miles)

Also, for emergency travel, the flexibility to change the return dates is pretty nice (while you do get that on a medical emergency fare, you don't with a advance purchase one, as was mentioned earlier.)

So, I've generally done better than $0.02/mile in my redemption. (And that's without factoring in the girlfriend gratitude factor, which is probably worth even more than $0.02/mile)

Dan