Madden NFL 12

Here's how I did it--you WILL have to go into Player Management in the rosters and change some stats, but that's not nearly as much of a hassle as you'd think.

1) Use Michael Vick. You may as well.
2) In his stats, simply turn everything that has to do with running and ballcarrying up to 99. You'll know what's what, and you won't be saving here, so it's not permanent.
3) This part is important--in a game (give each quarter a high time limit, just in case, and remember to set difficulty to "Rookie"), go into 'Settings' and 'Game Options', go to the bottom, and set 'Player Min Speed Threshold' to '0'. This will make player speed realistic--in other words, if the threshold was set to 100, even you (yes, YOU) could keep up with Vick in a footrace.
4) Go into 'CPU Skill' and make your opponent suck.
5) Your best chance at this is a play-action. (The play I used was 'PA WR In".) Since you lowered all the sliders in 'CPU Skill', the other team's defense will basically be looking at their shoelaces while you run past them. By the time they figure out it's not a running play, you should be 15 yards down.

EDIT: Oop, almost forgot--for those who don't know, if you want your QB to start running immediately press AND HOLD the right trigger (RT). I didn't know that myself first starting out--it's in the Manual from the Pause menu.

I think I have found an easier solution, that doesn't require any roster management fiddling (well, it can't hurt, but if you are halfway decent at the game it's really not necessary).

I used Tim Tebow (Denver Broncos) as the QB for this acheivement, not sure whether the same strategy can be applied to other QBs - perhaps not, given the acheivement title.

Get your team to somewhere within 40-50 yards of the endzone. When you get the opportunity to play call, go into the mini-menu (Ask Madden, By Formation, etc). Scroll to the bottom and choose 'By Player'. Tim Tebow should be automatically selected. When you go into his options, you have four or five running plays which use him in a half-back style role. On rookie difficulty opponents almost never suspect this, so if you run as soon as the ball has been hiked, you can, more often that not break right through to the end. I picked up 8 lengthy touchdowns this way in a 5min quarters game without editing, and also picked up the acheivements for QB running and for one player running the ball 200-or-so-yards.

Easy!