Not going back too far as that would belong on the Former Pro Player section.
1976-1977: Borg I guess
1978-1979: Borg by a ton
1980-1981: McEnroe
1982-1983: Connors
1984-1985: McEnroe, despite Lendl's superior 1985 and winning a slam in 84 and having a better year in 84 than McEnroe in 85. McEnroe's 84 was just amazing.
1986-1987: Lendl by a country mile
1988-1989: Becker for me, that is despite Lendl having a better (but fairly forgettable for both) 88. That is how much better I feel Becker was in 89.
1990-1991: Edberg
1992-1993: Courier easily
1994-1995: Sampras
1996-1997: Sampras
1998-1999: Sampras
2000-2001: Kuerten I guess
2002-2003: Agassi
2004-2005: Federer
2006-2007: Federer
2008-2009: Nadal
2010-2011: Nadal
2012-2013: Djokovic (?)
2014-2015: Djokovic
2016-2017: Nadal (?)
2018-2019: Djokovic
I strongly disagree with people putting Federer over Nadal for 2008-2009. Having watched poor years closely I have no doubt Nadal was further ahead of Federer in 2008 than Federer ahead of Nadal in 2009. Maybe not in slam results, but overall. Federer didn't even win a Masters title or anything outside his U.S Open in 2008. And really should have ended that year #3 behind Djokovic. Federer didn't even look for a moment like he would ever be #1 in 2009 until the huge French Open upset. Both have 3 slams, neither won the YEC, Federer has more slam finals but Nadal still reached the semis or better of 6 of 7 slams he played, and Nadal has a ton more Masters. Combining the two years it is Nadal easily for me. Plus as an earlier poster said wasn't the ATP points gap a lot more for Nadal in 2008 than Federer in 2009? Someone can confirm if this is true or false but it is how I remember it. At the very least it was more.
I also don't see how some of you are not putting Agassi for 2002-2003. Hewitt was tops in 2002 but garbage in 2003. Federer was nowhere in 2002. Roddick was nowhere in 2002. Agassi was a close #2 in 2002, and a close #4 in contention for #1 in 2003. The only knock is winning only 1 major, but guess what, nobody else won more than 1 either.
2012-2013 was a close call for me but I went with Djokovic. 2016-2017 was even tougher. You could make a case for any of Nadal, Federer, Djokovic, or Murray. And of course the common thread is each had only 1 good year.
2018-2019 was not that close for me. Nadal was nowhere near #1 at the end of 2018 unlike Djokovic in 2019 plus 1 more major. Plus Nadal barely winning tournaments (outside his 2 U.S Opens) never mind Masters or semi big tournaments outside of clay.