Latest ARM processors that are not BGA
Cavium Networks ECONA family has several ARM922-based processors with MMUs that run at 200-250 MHz. They have a PQFP 128-pin package. I think they're the most powerful non-BGA ARMs you can get (so far as I know).

PQFP packages are still pretty hairy to solder, so you might also look at the NXP 17xx series of Cortex M3 chips, which run at 100 MHz. Unfortunately, the M3 core does not have an MMU. I don't know all the packages used, but at least the LPC1758 comes in a LQFP 80-pin package with 0.5 mm pitch. You could also check the LPC2xxx series, but I'm not familiar with them.

If that's still too tricky, NXP has announced an ARM Cortex M0 chip, the LPC1114, that will be available in a 44-pin PLCC package in Q4 of 2010 (that is, you can't buy it for a few months yet). It only runs at 50 MHz and it has no MMU, but PLCCs can use through-hole sockets that can be soldered by hand pretty easily.  

update (2011-07-28, by stevenvh)
We're now 2011Q3, and there's no sign of a PLCC LPC1114; it's only available as LQFP48 and leadless HVQFN33. Frankly, it would have surprised me to see it in PLCC; it's an archaic and big package (height: 5mm!), which these days won't get many customers.