Just in the last month or so, a lot of the airlines have changed their fare structures. A lot of the "Saturday stay required" fares are gone, and it really doesn't matter when you travel. I travel a lot, and except for the occasional "Saturday stay" fares, I've rarely found any difference in fares based on the days of travel.
What will cause the fare to vary often, however, is the day you buy the ticket. NEVER buy an airline ticket on Friday, Saturday, or Sunday. Vacationers buy tickets then, and they jack up the prices for vacationers.
New pricing is usually posted shortly after midnight on Tuesday morning, so if you book early Tuesday you will usually have a wider selection of flight options and the lowest fares for that week. The more flexible you are with the time of the day, the better fare you will get.
It's a good idea to watch fares for a while. Look at Expedia, Travelocity, or Orbitz and see what the general fare levels are. Then, if they drop substantially below what they've been, you pounce.
My suggestion is NOT to buy your fare through one of those online travel agencies, though. The reason is, they may have the lowest fare available for a particular airline - but they'll only have one set of flights at that price. And that's going to be the beauty with four connections or a four-hour layover somewhere. If you check the airline's website, you will usually find a whole host of better flights at the same fare...occasionally lower, but never higher.