There are five major differences between the rules of college and professional football. There are a few other minor ones, but we'll just stick with the four main ones, and the minor ones have a barely noticeable effect on the game; in fact only rules experts are likely to even know about these minor differences, let alone notice them.
The first major rule difference is noticeable as soon as you look at a college field and then a pro field. The hash marks on the pro field are much narrower than those on a college field. This means that the pros tend to start each play pretty much in the middle of the field, and the hash marks don't tend to come into consideration much in terms of play calling.
In college, however, the wide hash marks have a few notable implications. One is that sweeps to the short side of the field run out of space really quickly, so coaches will often run to the wide side. Of course, if defenses expect that, then suddenly a run to the short side is a sneaky play. The time when it seems to matter most, however, is in the kicking game. In the college ranks, the wide hashes often mean that short field goals can be much more difficult than they would otherwise be, due to the sharp angle the kicker has to negotiate. In the pros, if you can kick the ball far and straight, you're probably going to make most of your attempts, but in college, a 20 yard field goal from the far left hash (or right if the kicker is left footed) can be a pretty imposing attempt, because the sharp angle reduces the apparent "open" area of the uprights.
Another major difference between college and the pros is related to clock management. In the college game, the clock stops whenever a first down is achieved, in order to allow the measurement crews time to reset their chains, whereas this action in the pros occurs with the clock running (unless the clock is stopped by some other game mechanic, such as going out of bounds). This of course gives the underdog a better chance of making a dramatic comeback, since they can essentially get free timeouts as long as they keep the ball moving.
The third major rules difference also relates to going out of bounds, but is related to what constitutes a legal pass reception. In the college ranks, you need to have control of the ball and get one foot down fully in-bounds to make a legal catch. In the pros, both feet are required. You will often see many of the better college receivers try to get both feet in, however, to show any pro scouts that might be watching, that they have the awareness to try to get both down. Essentially, this serves to widen the playing field a little bit in terms of the passing game.
The fourth primary rules difference that should be mentioned is the way each handles a game in which the score is tied at the end of regulation play. Both have an overtime period, but the rules of said overtime period are vastly different. The NFL uses a "sudden death" overtime system, in which a coin toss determines who receives the ball, and the first team to score wins.
The issue some have with that method is that it means there's a chance that one team gets no chance at all to have the ball, if the first team to get it scores immediately, the game is over. My retort is that team should have played better defense, but nonetheless, the college game attempts to rectify this perceived inadequacy with a more complex overtime scheme. Each team gets the ball on the opponents 25 yard line with 1st and 10. The team with the most points after these possessions is then declared the winner, if both teams score equally, the process is repeated until a winner is determined.
The final, and perhaps most important, difference between the two venues is that in college, if you have a knee down with the ball, the play is over, no matter what. In the NFL, you have to be forced down. In other words, if you are a running back making a cut up the field, and slip and fall, in the NFL you can get up and keep running. The play is still live until someone touches while down. In the college game, the play is over.
It's always funny to see NFL rookies forget this rule. I remember when Plaxico Burress was a rookie wide receiver for the Steelers, he caught a long pass of 40 yards or so, but had to dive and get it, and so was laying on the ground when he caught it. He got up and celebrated his good play, and spiked the ball triumphantly in the turf. Suddenly Plaxico's good play turned into a bonehead play; the live ball Plax "fumbled" was recovered by the defense.
This very vividly underscores the importance of knowing the differences in the rules of the game you're playing. In college, that would indeed have been a great play. In the pros, he is the goat for the game. Burress should have leaped back to his feet and kept running for the end zone, instead he created a major turnover that got him on Sportscenter for all the WRONG reasons.