Without further ado, here we go:

England (Premier League): an easy choice, no doubt Leicester City's 2015-16 Premier League title is probably the wildest, most random league title ever won. They were promoted just 2 seasons before this title, finished 14th the prior season, and have never finished above 9th ever since.
Spain (La Liga): one of the stranger entries on the La Liga title list was Deportivo La Coruña, winning the 1999-2000 La Liga title. They hadn't won a league title beforehand and just suddenly appeared on the map. They were helped by Real Madrid finishing 5th but had to battle Barcelona for the top spot.
Italy (Serie A): this one's tough because after AS Roma's Serie A title in 2000-2001, only three clubs (Juventus, Inter Milan, and AC Milan) have won the Serie A. But combined with Lazio's 1999-2000 title the season before, it's worth noting that this was a rare instance in modern Italian football where Juventus, Inter Milan, and AC Milan were out of the league title in back-to-back years.
Germany (Bundesliga): has to be VfL Wolfsburg winning the league in 2008-09. They had been a middling to just downright bad team before this title, and they fell back into suckitude afterward.
France (Ligue 1): Montepellier winning the 2011-12 Ligue 1 title was quite random. Like VfL Wolfsburg, they rose up from suckitude this one year, then fell back into it right afterward. Still a great run though.
Portugal (Primeira Liga): basically, if you're not a fan of Benfica, Sporting, or Porto, you're going to have a tough life (well, maybe add Sporting on the heartbreak list as well due to their league title drought). Some club named Boavista just randomly won the league, however, in 2000-01. Although it was only the second season of the Primeira Liga, it's important to note that they are only one of two clubs (the other being Belenenses back in freaking 1946) outside of the Big 3 to win the league. Since then, Boavista has not had the same success, even suffering relegation.
Netherlands (Eredivisie): Ajax and PSV Eindhoven have owned this league since the turn of the millennium. But no one's perfect, and both clubs were humbled two years in a row in 2008-09 and 2009-10 when AZ (only one league title back in 1980-81) and FC Twente (no titles previously) won those titles respectively. I would also include Feyenoord's 2016-17 title, but they already had 14 league titles before then.
Scotland (Scottish Premier League): sorry, none in recent memory. The last non-Celtic/Rangers title was won in 1984-85 by Aberdeen. What league parity?
Greece (Super League Greece): make way for the new kids on the block. After years of dominance by primarily Olympiacos with some hiccups to Panathinaikos, AEK put themselves back on the map in 2017-18 and PAOK scored a rare Super League title the following season. My nod goes to PAOK though: they had only won two titles before that season.
Belgium (First Division A): all I know is that some random team named K.A.A. Gent just randomly won their first league title in 115 years in 2014-15. Of all the football leagues in Europe, however, Belgium may have one of the higher parities between clubs.

OK, time to stop. I could go on and on, but I think I've covered (most) of the highlights.

how time flies.... Leicester City was.....