Inspired by ephram's musical mock and HungryStripes's suggestion of a sitcom based draft. Here's something that will hopefully keep people entertained for the next 10 hours or so.
1. New York Giants (From Houston Texans) - Seinfeld
The Giants trade all their 2014 and 2015 picks to move up to the top of the draft and grab a once-in-a-lifetime prospect.
2. St. Louis Rams - M*A*S*H*
The NFC West is a war-zone and when placed in a situation like that, the best thing to do is laugh.
3. Jacksonville Jaguars - Simpsons
There is an area of Jacksonville called Springfield and The Simpsons are more than deserving of selection at this position.
4. Cleveland Browns - Soap
The on-going nonsensical soap opera that is the Cleveland Browns make an obvious choice here.
5. Oakland Raiders - Blackadder
A surprise pick, although that's the norm for the Raiders, the Black Hole get to cheer on the devious and cunning Blackadder.
6. Atlanta Falcons - Archer
Perhaps something of a reach but the Falcons can't resist pairing Matty Ice with the cool-as-ice Archer. Also made in Atlanta.
7. Tampa Bay Buccaneers - Gilligan's Island
The Bucs have a rag-tag bunch of castaways on their roster, making this a perfect fit. Plus the name and everything.
8. Minnesota Vikings - Arrested Development
No other choice for the team boasting the most NFL player arrests since 2000.
9. Buffalo Bills - Trailer Park Boys
A not so subtle attempt to tap into the Canadian market for the Bills.
10. Detroit Lions - Home Improvement
Set in Detroit and featuring a jokey, over-confident protagonist. No parallels there...
11. Tennessee Titans - Friends
A vanilla pick for a vanilla franchise.
12. Houston Texans (From New York Giants) - Beavis and Butt-head
The troublesome Texan teens head to the NFL's youngest franchise.
13. St. Louis Rams - Family Guy
A once fresh and exciting team struggles to recapture its heyday.
14. Chicago Bears - The Bob Newhart Show
Quintessential Chicago, old school and no nonsense.
15. Pittsburgh Steelers - The Office (U.S.)
Set in Scranton not Pittsburgh but close enough. Draw all the Tomlin-Scott inferences you want.
16. Dallas Cowboys - King of the Hill
Mike Judge makes his second appearance going to a Texas team. I like to think that 'King of the Hill' is also how Jerry Jones refers to himself.
17. Baltimore Ravens - Veep
Selina Meyer is a former Maryland senator. A begrudgingly great pick for the Ravens.
18. New York Jets - 30 Rock
A decisive and controlling authority figure that wants to oversee everything?
19. Miami Dolphins - Golden Girls
They've both seen better days.
20. Arizona Cardinals - Curb Your Enthusiasm
Much like Larry David, Carson always knows how to make a bad situation worse.
21. Green Bay Packers - Happy Days
Wisconsin's most famous export. The Favre also jumped the shark with his multiple non-retirements.
22. Philadelphia Eagles - It's Always Sunny In Philadelphia
No brainer. BPA and fills a need.
23. Kansas City Chiefs - Grace Under Fire
It was set in Missouri, that's about all I have to say about this pick.
24. Cincinnati Bengals - WKRP in Cincinnati
Unlike the real draft, a pretty much consensus pick for the Bengals.
25. San Diego Chargers - Weeds
The Chargers take a punt on a boom-or-bust hometown prospect with substance 'issues'.
26. Cleveland Browns - The Drew Carey Show
The Browns surprise everybody by making a solid, unadventurous pick.
27. New Orleans Saints - The Ren & Stimpy Show
Ren & Stimpy. Peyton & Ryan.
28. Carolina Panthers - The Andy Griffith Show
A great value pick celebrated all across North Carolina.
29. New England Patriots - Cheers
The Patriots manage to find a future HOF player at the bottom of the first.
30. San Francisco 49ers - Full House
The 49ers roster is packed with talent and much like the Olsen twins they have the Smith...twins.
31. Denver Broncos - South Park
Well, you've got to look out for your kids, right?
32. Seattle Seahawks - Frasier
A constant lack of sobriety has seen this former number one prospect slide to the bottom of the round.