• Cunningham numbers
• Homogeneous Cunninghams (numbers of the form aⁿ ± bⁿ)
• (Generalized) Cullen and Woodall numbers
• factorials ± 1 (My tables of factors of N!+1 and N!-1 go only as far as N = 400.)
• the HP(49) problem
• Mersenne numbers, which all take the form 2ⁿ-1.  The Cunningham 2- table contains small Mersenne numbers. My table has prime exponents up to 10000 and mersenne.org has lots more information on Mersenne numbers.
• Numbers of the  form x^y + y^x.

Paul Zimmermann is running ECMNET which is another distributed factoring project. It uses Lenstra's Elliptic Curve Method to find relatively small (up to 55 digits or so) factors of integers. Many people run the programs "by hand". For those who prefer an easier life, Tim Charron wrote a client/server harness to ECMNET so that the computation may proceed without human intervention. I am running two ECMNET servers on the IP address 83.217.167.177. That which is running on port 8194 is currently loaded up with the (Generalized) Cullen and Woodall numbers, whereas that on port 8195 is loaded with the Homogeneous Cunninghams.