Montpellier was just about as shocking as Leicester, and there was one in Turkey where a mid/lower league table won it a few years ago. Fairly sure absolutely no one expected Atletico to actually win their first title 2 (?) years ago as well. Denmark winning the Euro's after failing to qualify is also a thing, as is Greece being chosen as the outsider for even exiting the groups, but managing to win the tournament.
Remember when Chelsea were failing miserably in the league, so they got Di Matteo in, who managed to win the CL against all odds?
Sports overall: I heard last year around the Grand National that there'd been a horserace in the mid 90s where the jockey was at something ridiculous like 25000/1 and managed to win it, I think that's slightly more shocking. Loads of olympic sports have random champions nowadays as well, it's great fun and variety imo.
Loads of near-wins as well (as, sadly, you're still not as nailed on for it tbh), so...
To add to other posters fair enough and all good, valid examples. I think one off tournaments like the euros don't come close really as it's going undefeated after a group stage and is what 6/7 matches in total. Leicester will be 9 months! Again a horse race is a one off, especially a national where the favourite rarely wins.
The Forest one is a good shout that they went on to win in Europe.
As a total unexpected shock though I genuinely think Leicester because one off tournaments in sports where you play 5-8 matches isn't comparable in going a year almost in holding off competition. Just my opinion.