Paying a broker costs roughly a month of rent, so even if the value of your time is $200/hour, you're coming out ahead by doing the work yourself. I've had luck with both pay-to-play aggregators like http://www.rdny.com, as well as blind Google searching. Friends of mine have also done free aggregators like streetyeasy, and one even just showed up to a building and asked about free listings.
This is useful if you want to rent an apartment, not a specific apartment. Many apartments only go through brokers. I don't think that's a good-enough argument to go with one.