I'll try to throw out some names that haven't already been mentioned:
QB: Chad Henne (last-round special) - The Jags will be forced to throw the ball a fair amount in 2014, even if most of that is in garbage time. The Jags collected skill-position players in FA and the draft like they were building their own fantasy team. The Jags' 1st-round pick is widely regarded as a project QB whom even their own front office hopes doesn't have to start year 1. Riddle me this: why is the Jags' presumptive starting QB going nearly undrafted? At today's ADPs, you can pick up Rivers or Cutler in the 9th, add Henne in, oh, the 18th, and be broadly competitive at the position against owners who drop a 3rd and a 10th.
RB: Jeremy Hill - Steps in as a bruiser and a possible GL back for an OC whose philosophy will be run it, then run it, then run it some more. Ought to take him about 27 seconds to beat out BJGE in camp. Unlike most backs going around his ADP (RB50 or so), Hill doesn't need to count on injury / ineffectiveness; he could put up RB3-type numbers even with a completely healthy Gio in the mix.
WR:
Aaron Dobson - There is a 0% chance that Julian Edelman gets 175 targets again this season, and Amendola isn't getting any younger (or more durable). Classic case of (IMO) a middling talent who can make the most of a great situation in NE and if so will outperform his ADP by 3-4 rounds.
Jerricho Cotchery - Kelvin Benjamin has "bust" written all over him IMO, but even if he isn't the next Stephen Hill, I don't expect miracles to happen right out of the gate. Cotchery (ADP of around #200) should make a strong play to lead the team in receptions - on the one hand, being a team's leading WR does not a fantasy stud make (says the 2013 Jeremy Kerley owner), but on the other hand, Cam Newton >>>>> Geno Smith.
TE: Travis Kelce - Sorry, can't help but add to the echo chamber here. Microfracture surgery is tricky, but we should know one way or another whether he's back to 100% by August. Besides the benefit of Alex Smith needing a safety blanket, he's also working under one of the TE-friendliest systems around (under Andy Reid, a.k.a. "the guy who made Brent Celek fantasy-relevant"). This seems like it could be a great year to punt on TE and scoop up two or three young guys like Kelce / L. Green / Clay / Eifert in the TE15-20 range.