Fouling gets some bad press in the forums, but it is an aspect to a good coaches Blood Bowl game. Even if you are determined not to foul yourself, it is useful to know the mindset of coaches who foul.

Some simple truths to start with.
A player who can't be knocked down, can't be fouled.
A player who is out of range of all opposing players can't be fouled.
A player who can't be encircled can't be fouled effectively.

The potential benefit to fouling is that you may get a player off of the pitch, or at least down for an extra turn. Some players are abominations that can turn the game against you. Could be a 1 turn TD machine, or Claw/RSC monster, or a Dirty Player. If you "play fair" and don't stomp such players, the game is much more likely to go against you. In fact if you don't stomp every RSC you see, you are evil. A team can't get to 2-3 RSC if every time they get one it gets pulped.

The risk is getting spotted by the ref, loosing a player, and suffering a turnover all at the same time. This risk is 1 in 6 if the ref is not watching you, and 1 in 2 if he is. I couldn't be bothered adjusting for arguing with the ref.

EDIT: Koigokuro could be bothered. His figures are
"It's 5/36 without eye and 15/36 with the eye if you have coach arguing."

The cost is that your fouling player(s) aren't doing anything else that turn.

If your opponent isn't fouling, then you only get two low risk shots per match, so making them count is important. If your opponent is fouling, then you get more low risk shots, however, it may be dumb to take them. If he's fouling smart with a gang of assists, then fouling back without assists is a mug's game. If he's fouling your chaos warriors, then fouling his linemen is a poor trade. You give your opponents gang more low risk shots that he's making count, in return for your low risk shots that you aren't making count. If you can't get the position to have a high chance of getting through his armour with your foul, it is probably not worth doing. If he wants to foul that badly, let him get his players sent off.

Assuming you have the position to foul, consider the risk, If every other player on your team has already moved, you've insulated yourself from the turnover risk. All you have to ask yourself then is whether the player that might be injured is worth more than the player that might be sent off. Having three green linemen sent off is probably worth it to get a Claw/RSC player off the pitch. If you get a kill, tell the IRC channel, only one coach ever mourns the death of a Claw/RSC player. The rest celebrate.

The strategy of "foul 'em all" deserves a mention. It's entirely valid and within the rules to thin out your opponent's numbers in an attempt to force your opponent to have to line up his weaker players, or the munchkins you really want rid of, on the front line. It is devious, but that doesn't make it either evil or illegal.

The most unorthodox reason I've ever had for fouling was in a match where my team was getting murdered. I started fouling in an attempt to get my most experienced players sent off. While I lost the game, I was able to finish it without conceding safe in the knowledge that I'd have the players I couldn't replace easily fresh for the next match. If I'd let them get mauled by the opposition instead, I'd have only had a 1 in 2 chance of having them for the next match. Of course I still had to find I player I could fell in order to foul him. Strange thing was, my opponent had got the ref, but stopped fouling. I guess he figured I was getting my own players off the pitch faster than he could.

Finally, there's the strategic question of whether to invest a skill roll in a Dirty Player. I consider it unnecessary until you get to 14 players or so on the roster, because if there's a player that needs to go down, it's worth devoting your entire team to the effort in a gang foul. With a Dirty Player you need less assists, and you have more chance of getting your victim off the pitch in a mass foul. Once you get to 14 players, or about TR175 it's definitely worth having a Dirty Player on the roster. Even from the reserves box he can make your opponent think twice about how dirty he wants the match to get. Especially if he doesn't have one.

EDIT: CircularLogic disagrees and reckons:
"In game 2, where other teams have only 11 players and/or no apo such a tool [a Dirty Player] is way more powerful, than if a team has a deep bench+apo to negate the first good foul."
CircularLogic's rating is way better than mine, and he says more in the comments

EDIT: Kharnete pointed out paulhicks' guide:
http://fumbbl.com/FUMBBL.php?page=blog&coach=13020
I also suggest this as further reading.

Since you've read to here I wish you happy fouling if you are a fouler, and happy foul-assist spoiling if you are still devotedly anti-foul. Whatever your choice, fight well, and may Nuffle bless your teams.