I think a top 10 11 should about cover it. I'll echo @CS85's thoughts about watching a team you love fall apart just like you knew they would. This last weekend's Bears games was the epitome of that feeling, but in terms of specific days, here's my list.
11. September 9, 2018: Packers vs Bears. This will be a theme throughout the list. Aaron Rodgers is my least favorite human being in the entire scope of history. I hate his precision, I hate his stupid smug face, I hate his State Farm commercials, but most of all I hate the inevitability that he will beat the Bears. No lead is safe, no team is good enough to beat this man, and I'm doomed to watch him slice through our defense for the rest of time.
10. April 28, 2012: Derrick Rose tears his ACL vs. the 76ers. I didn't realize the consequences of this at the time, but the aftermath and being robbed of one of the most entertaining players I've ever seen hurts quite a bit.
9. November 10, 2014: Packers vs. Bears. Aaron Rodgers throws 6 touchdowns in the first half against the worst Bears defense I have ever seen. This loss came immediately after getting curbstomped by the Patriots the previous week. I don't think I've ever cheered for a worse team than that one.
8. February 7, 2007: Super Bowl XLI. For whatever reason this loss doesn't bother me as much as the more recent Bears disasters, as I was just happy to be there. Still not a great feeling to lose the Super Bowl.
7. April 4, 2005: Illinois loses to North Carolina in the National Championship. I was five years old when this happened, and this was the first team that I ever really got into. Dee Brown and Deron Williams were my heroes. I remember my parents finally letting me stay up long enough to watch the end, and being absolutely devestated when they lost. I think this was the most I cried over a single sporting event.
6. May 10, 2015: Lebron buzzer beater in Game 4 vs. the Bulls. For as much as I hate Aaron Rodgers, Lebron is right up there in terms of always beating my team. After the Rose buzzer beater in the previous game I thought this time would be different, but as soon as Lebron pulled up for the shot I knew this series was over.
5. June 1, 2014: Blackhawks vs. Kings Game 7. I'll admit that this loss doesn't hurt that much in the context of winning three Stanley Cups, but losing in overtime in Game 7 is always heartbreaking.
4. October 10, 2017: The USMNT loses to Trinidad & Tobago to miss the World Cup. Something that should never have happened, but something we totally deserved. We still haven't recovered from the aftermath, and I'm questioning whether we ever will.
3. January 23, 2011: NFC Championship Game: The next-closest the Bears had come to winning it all. This one didn't hurt quite so much as I thought it would as I was still fairly young and the pain felt duller than the #2 and #1. This game wasn't taken from us at the last moment, instead I was forced to watch us slowly fall short as Caleb Hainie threw a pass to BJ Raji for no apparent reason. Seeing the Packers win it all two weeks later hurt even more.
2. December 29, 2013: Aaron Rodgers 4th & 8 to Randall Cobb. Those same damn Packers. The day Aaron Rodgers finally retires will instantly hit the top ten of my best days of my life as a sports fan.
1. January 6, 2019: Cody Parkey Double Doink. Especially in the context of this season to see the first good Bears team in years fall apart in the most predictable way possible was heartbreaking. That was our shot at the Super Bowl, as it's clear that whatever worked last year is now gone.