Sportsbook house rules, sport by sport
Every book has a rules page, and almost nobody reads it until a bet is graded in a way they didn't expect. Below are the rules most books share. Your book's own page is the one that counts, so read it before the first bet, not after the argument.
The ticket is the bet
Start with the rule that covers everything. Once a book accepts and confirms your bet, it stands at the price and the number on the ticket, whatever the line does afterwards. Most books won't change or cancel a confirmed ticket, and if there is an argument about when a bet went in, they go by the time stamp in their own log, not by your memory of it.
So check the team, the number and the stake before you press the button. I've watched players take the wrong side in a hurry, and no book I know of gives that back. The other half of the rule protects you: if the line moves after you bet, that is the book's problem.
Most books also keep the right to void a bet taken at a plainly wrong price (see why a sportsbook voids a wager). A game moved to another venue is often graded no action, and one postponed beyond the window the book sets is usually void.
Football
Most books treat a football game as official once 55 minutes have been played. If it is stopped before that, sides and totals are usually void, though a bet on a half or quarter that was already finished still stands.
Overtime counts. It is part of the full game for the spread, the moneyline and the total, and most books count it in the second half as well. It usually does not count in the fourth quarter: a fourth-quarter bet is graded at the end of regulation.
Player props are usually graded on the league's official statistics, overtime included. The novelty props (the coin toss, the anthem, the colour of the drink poured on the coach) are graded at the book's discretion, which is a polite way of saying they decide. I'd stick to props a box score can settle.
Basketball
The professional game is usually official once 43 minutes have been played, which means no more than five minutes left. In college the same five-minute rule usually applies to a 40-minute game, so 35 minutes.
Overtime counts toward the full game and the second half, and, as in football, fourth-quarter bets are usually settled at the end of regulation. A half or quarter bet needs that period finished to have action.
Hockey
In hockey the rule to know is the shootout. Most books count overtime and the shootout on the moneyline, and when a shootout decides it they add one goal to the winner's score, however many shots went in.
Look at what that does to the puck line. A game decided in a shootout ends with the winner one goal ahead, so a favorite at -1.5 never covers that way and the underdog at +1.5 always does. Most books also leave shootout goals out of goal props and player points.
A three-way moneyline is the exception: it is a bet on regulation only, so a tie after 60 minutes wins the draw.
Baseball
Most books need five innings for a full-game bet to have action, or four and a half if the home team is ahead. Prices are usually tied to the listed starting pitchers, and if one of them doesn't start, the bet is void unless you chose "action" when you placed it. I'd keep the listed pitchers on, because the price you took was made for the man who was meant to pitch.
Golf
An outright or a matchup usually needs 54 holes played for action. A player who doesn't tee off is usually a void bet. One who tees off and then withdraws usually loses on an outright, and in a matchup the other player is usually graded the winner.
Ties are the rule people miss. On top-10, top-20 and group bets most books use dead-heat rules: your stake is divided by the number of players tied for the last places. Say you bet $100 on a player to finish in the top 10 at +200 and he ties with one other man for 10th. Half your stake, $50, is paid at +200 and wins $100, so $150 comes back. The other $50 loses. You won $50 on a bet you thought had won $200.
Horse racing
A sportsbook price on a big race is fixed when you take it. A racebook pays the track's pool price at post time, the way off-track betting always has. The difference matters when a horse is scratched: a straight bet in the racebook on a scratched horse is usually refunded, while a futures bet in the sportsbook usually loses. Some racebooks also cap what they will pay on exotics, whatever the track pays, so a big trifecta can come back smaller than the track's figure.
Before you bet
None of this is hidden; it sits on a page few players open. I'd read the rules for each sport the first time you bet it at a new book, and again for anything unusual (a half, a prop, a golfer), because that is where books differ most.
And bet the way you can afford to lose it, rules or no rules. A dead heat or a shootout can take a winner away from you, and money you needed was never the right money to bet.