As a regular traveller, hunting cheap ticket is like a passion and hobby for me. I've found 200+ euro return tickets from Europe to Asia a couple of times, also have found business class tickets for economy price (600-700 euro range).
I'm using flyerstalk forum a lot, where a lot of frequent travellers hunt cheap tickets. There are tons of website offering so called error fare tickets, such as secretflying etc. But of course you will have to be lucky and spontaneous in this case.
Otherwise, have you heard about ITA Matrix power by google? A good tool especially for open-jaw tickets. Or websites like kiwi.com, momondo also pretty decent if you are not used to ITA matrix's UI.
Oooh these seem like great tips. Thanks! I feel like one of these days I'll pick a flight and a location just whatever is cheapest and see what happens!