This is in no way a prediction to what teams will actually do. I cannot stress that enough.
I'm not exactly a BPA guy but I don't stray far in most cases. In general I have a top 3 needs list for each team and I usually go with the BPA from that grouping unless there's a clearly better talent (IMO) available at a spot who I think can make a better impact on the team.
I've had a bit of a philosophical change; I'm less averse to taking a shot at a higher risk/higher reward talent in the 1st round than I used to be. The lower rookie contracts help, as does my growing perception that impact players at impact positions are more important than just very good players who might be safer picks. It's a hard balance for me because I'm generally much better at figuring out who is going to be unexpectedly awful than I am who is going to be unexpectedly great. We all have our plusses and minuses

The top 10
Round 1
1. Indianapolis Colts: Andrew Luck, QB, Stanford. RG3 might have a higher ceiling, but I'm more confident that Luck will hit his lofty ceiling. He is as can't miss as any player I've ever seen and the type of guy you dream about building a franchise around.
2. Washington Redskins (from STL): Robert Griffin III, QB, Baylor. I believe that the Skins need a franchise identity more than anything. RG3 can be that identity. This transcends whatever he might do on the field, and what he does on the field has the chance to be very special in its own right.
3. Minnesota Vikings: Morris Claiborne, CB, LSU. I'm a firm advocate of building to win your own division. The NFC North features Calvin Johnson, Greg Jennings and Brandon Marshall, and right now the only viable CB on the Vikings is 34-year-old Antoine Winfield. Claiborne brings potential lockdown corner ability. His wrist surgery does not concern me.
4. Cleveland Browns: Melvin Ingram, DE, South Carolina. The concept of pairing Ingram with last year's excellent rookie Jabaal Sheard gives the Browns young bookend pass rushers that can really create headaches for opposing offenses. This move would give them a better chance to compete right now, as Tannehill isn't yet ready at QB and I'm not sold enough on any of the wideouts here. The extra first round pick gives lots of leverage to take the best impact talent here, and Ingram is that player for this defense.
5. Tampa Bay Buccaneers: Trent Richardson, RB, Alabama. I'll admit to having several names listed here before "settling" on Richardson. In the end I went with the player who I think best gives their division opponents problems. I've never been a believer in Legarrette Blount either. As I've said for months now, Richardson reminds me of a young Eddie George, only faster. That kind of threat in the backfield gives the Tampa offense balance and eases the pressure off Josh Freeman to try and win games on his own, which did not work too well a year ago.
6. St. Louis Rams (from WAS): Michael Floyd, WR, Notre Dame. Floyd is the top WR on my draft board and the Rams need to surround Sam Bradford will all the talent they can. I prefer Floyd's size and downfield prowess to Justin Blackmon in this offense, though it's not an easy choice. I would take Ingram or Claiborne if they were still available.
7. Jacksonville Jaguars: Justin Blackmon, WR, Oklahoma State. The physical Blackmon is a nice fit with Blaine Gabbert, a QB that likes to (and needs to) get the ball out quickly on shorter routes. Blackmon is the kind of receiver that can turn a simple slant into a big play. He's also got a manic wildness to him that can provide this staid offense with some needed energy and panache. Selling more tickets has to factor into the draft equation or else this will be the LA Jaguars before 2015.
8. Miami Dolphins: Ryan Tannehill, QB, Texas A&M. Patience is rewarded and the Dolphins get the franchise QB they so desperately covet. Honestly if Tannehill is still on the board there really isn't an option but to take him, or else the owner is going to fire the GM. Since I'm playing GM, this one is about self-preservation as much as making my team better. I actually prefer Tannehill to Sam Bradford--just not in 2012--and Matt Moore makes a solid bridge.
9. Carolina Panthers: Dontari Poe, DT, Memphis. He's wrongly miscast by many as a nose tackle, but Poe is a 4-3 3-technique with awesome size. He needs some development but Carolina has the coaching staff to make that happen. Poe can turn the biggest weakness--interior defense--into an asset. This was one of the easier picks of the round for me.
10. Buffalo Bills: Matt Kalil, T, USC. I'm more bearish on Kalil than most, but he is the best tackle in this draft and represents strong value here. It says a lot that no teams have rushed to sign free agent Demetrius Bell, the erstwhile starting LT in Buffalo. Kalil is smart and ready to start right away. GM Buddy Nix has publicly declared a desire to get better at tackle, and I agree. I was hoping Tannehill would fall here as a developmental/insurance policy.