Let's look at the 2013 draft class.
QB I see one first round QB, Clyde Phillips. He's volatile so there is a good bust probability but someone will pick him and take a chance. Robert Hadsell could get picked if someone doesn't mind 80/100 accuracy.
RB There is some speed at the top of the RB class. Jason Fletcher and Sean Sheffield should be top of the draft picks but there are others with 80+ speed available.
TE Ronald Hoover should be the 1st TE off the board. He has 74 speed at 259 lbs so he won't be overly fast if he moves to RB or WR. He's an excellent blocker so he's probably best suited to stay at TE but that's just my 2 cents. Ezra Few has the speed to possibly be a 1st round pick as well, though his skills don't seem to be as good as Hoover.
WR I counted 9 WR prospects with 80+ speed and rated at least 75 by my weights. While it might be a bad year to need a QB, it looks like there is some speedy skill position options for us.
OL I see 2 non centers worthy of a 1st, Bryan Pereira and Michael McDonald. There are 3 centers that could also get picked if someone has a need. The next level of OL is plentiful so I expect most of them will get picked in rounds 2 and 3.
DE/DT Not a good year for defensive line. I only have 5 rated 70 or higher and only 2 have 70+ speed.
LB Linebacker is almost as thin as DL, though there are a couple more rated 70+ than at DL. A couple have good speed. Doesn't seem to be a particularly deep position either.
DB There are a few options at the top that provide speed and skills but they will go quickly and there isn't much depth available. If you want one you'll need to grab one early.
K/P I see no kickers worth drafting and just 1 punter.