It depends what you want. If you want a package holiday then the Travel Agents can be best, but if you're looking to fly out, have a DIY holiday and then fly home, hit the price comparison websites, every single one, and then take that as a starting point.
I fly to Canada quite often because my gf is Canadian, I have a couple of times managed to find cheap flights on very odd airlines that have been great flights, other times they've been awful, but if you're looking to fly to Europe then at least you won't be on the plane too long
So yeah, lots of price checking, call around if you're good at arguing on the phone (I'm not) and you can often get discounts. And Always ALWAYS book well in advance!