The Royals have the longest drought in the majors for both Cycles (1990) and Triple Plays (2006) and are third in No Hitters (1991).
Longest active no-hitter droughts:
Cleveland 1981
Toronto 1990
\*Kansas City\* 1991
Longest active cycle droughts:
\*Kansas City\* 1990
Detroit 2006
Oakland 2007
Longest active triple-play droughts:
\*Kansas City\* 2006
San Francisco 2008
Arizona 2009
As a Royals fan, this is extremely annoying. Noah Cameron took a no hitter into the 7th today, but of course, that's as far as it went. And in fact, opponents have a hard time doing any of these things against the Royals either. Since 2009, there have only been two opponent triple plays turned against the Royals, and no No Hitters or Cycles. The next-lowest number of such events in a team's games since 2009 is 6 (Cardinals) and the highest number is 19 (Astros).
Every MLB team has done at least one of the above since 2016 (Pittsburgh's most recent cycle was in 2016) except for the Royals, who haven't done one since 2006. I'm kind of rooting for Cleveland and Toronto to throw no hitters soon, just to see the Royals at the top of all three droughts.