Crisis on Infinite Earths
Beginning in April 1985 for 12 issues, this was a crossover event that restructured the DC Universe. In addition many of DC's titles had crossover stories. The Reading list can be found here. This was followed by Zero Hour: Crisis in Time in 1994.
Crisis on Multiple Earths
This is an anthology series from July 2002 featuring Justice League of America and Justice Society of America. I'm not certain how it affects the Crisis on Infinite Earths storyline. Info can be found here.
Identity Crisis
A seven issues series from 2004 and 2005. More info can be found here.
Countdown to Infinite Crisis
This is a separate crossover event beginning in May 2005. There is one issue with this title and the remainder of the storyline is printed in various DC titles. The reading list is shown here . This storyline was the lead up to Infinite Crisis.
Infinite Crisis
Another crossover event throughout DC comics titles that were published in 2005 and 2006. There are seven issues in the Infinite Crisis titled series, plus numerous crossover issues in other titles. The reading list can be found here. This is the storyline that kills off the Ryan Kendall version of Black Condor, which I thought was a poor decision on DC's part.
Final Crisis
This is a comic series that ran for seven issues in 2008 and 2009. There are also crossover issues. More info can be found here.
Dark Crisis on Infinite Earths
This was announced in 2022 and will continue into 2023. I'm only guessing here, but I think maybe, just maybe, this might be.... oh, I dunno.... a DC universe shifting event with lots of cross overs. I could be terribly mistaken though. Info can be found here.
Okay, enough with having a crisis already! LOL I think DC comics is having a crisis of creativity! Doesn't "Final Crisis" mean anything? This is just like KISS after their farewell tour! LOL I love DC Comics but this whole Crisis thing has been flogged to death. They might as well just start calling it "DC Comics Semi-Annual Crisis Fundraiser".