Brilliant. For those situations where a binary and equally likely outcomes, it's ideal.
Perhaps the classic case of a coin toss deciding the outcome of cricket match was the first test in the 1950/51 series between Australia and England.
Australia batted first, and scored 228, a very creditable performance by the England bowlers.
Then it rained, and the pitch became a "sticky dog", basically unplayable by batsmen. The ball, when it pitched, could do anything - scuttle along the ground, rear up, turn sharply, and there was no way of predicting which. England batted, reached 68/7, and the England captain declared, hoping to catch Australia on the same impossible pitch, and hope that the pitch improved by the time England batted again. Hasset, the Australian captain, was wise to this, and declared at 32/7. The pitch was still impossible, and despite the innings of a lifetime by Hutton, who never played better for a mere 62 not out, England were all out for 122.
Of course the first stock image uses a (two-)euro coin
I could have written a lot more about this - for example the reason why Hewlett-Packard isn't Packard-Hewlett is also because of a coin toss, but maybe that one would come better under some corporate-themed articles I'm pondering.
Hopefully the sports stuff didn't have any errors, very much writing outside my comfort zone there. As David F says, of course, plenty more examples I didn't cover.
The FIFA World Cup group stages still use tossing a coin as a tiebreaker of last resort - this has actually happened three times, twice in 1954 and once in 1990, but only to determine which slot each would have between two teams going through to the next stage.
However, the 1954 ones in particular arguably still had a major impact - Hungary had to literally fight Brazil in the so-called Battle of Berne in the quarter-finals, and went to extra time against holders Uruguay in the semis, before the final saw them face a West Germany who had cruised past Yugoslavia and thrashed Austria, and Hungary being more exhausted has been cited (amongst many others) as a reason why what some (especially in Hungary) would argue was the best team to ever enter a World Cup ultimately lost 3-2. The Brazil/Yugoslavia and Uruguay/Austria coin tosses going the other way would have resulted in the opposite matchups (well, it's quite likely Hungary would have ended up facing England in the semis, and not impossible West Germany would have hosts Switzerland, and of course that's assuming both went through), though given the, er, decidedly oddball rules of the 1954 World Cup one could reasonably argue Hungary having the tougher side of the draw was exactly as intended.
A lot of records that still stand were also set that year and would obviously be affected.