Suppose $N$ is an RSA modulus (ie, it's the product of two distinct primes), 256 bits long. What is the best method to factor it?
Trial division is out of the question, Pollard's Rho is probably out as well (without significant parallelization). I doubt there are any online tools or math libraries that can handle this number (I think Wolfram Alpha uses Pollard's Rho algorithm).
Moduli up to 768 bits have been factored, and RSA Corp's (now defunct) challenge list doesn't even address numbers as small as 256 bits, so it must be pretty easy... but how?
The comment left by Dave R gives the best answer: ECM is outdone by SIQS for the semiprimes of interest and there are several freely-available implementations of SIQS. The one Dave R gives at http://www.alpertron.com.ar/ECM.HTM factors numbers of 256-bits in about 4 mins on my Dual-Core 2.8GHz Windows XP: set number of processors to 2 and set "New Curve" to zero in order to force SIQS (ECM will generally not help for semiprimes of this size).