Edge of factoring technology? Schneier in 1996's Applied Cryptography says: 

"Currently, a 129-decimal-digit
  modulus is at the edge of factoring
  technology"

In the intervening 15 years has anything much changed?

For factoring RSA moduli (product of two large distinct primes), the Number Field Sieve is still king.  It has two phases: a parallelizable sieving phase where we look for polynomials, then a non-parallelizable matrix reduction step that is usually done on a large computer.
If quantum computers ever become practical, they can factor integers via Shor's algorithm in polynomial time.  In fact, this is the only known compelling application for them, but it's enough for the military to spend millions in the U.S. funding research on quantum computers.
Note: Peter Shor is a frequent contributor on this site.
