Cubs have the longest championship round appearance drought of the 4 major team sports at 67 seasons now.
The Sacramento Kings are 2nd - their last NBA finals appearance came 62 seasons ago.
The Atlanta Hawks and Detroit Lions are tied for 3rd at 55 seasons.
All others are 45 seasons or less.
You can't really make legitimate comparisons like that between the teams in different sports because the sports historically are different and have different formats which have changed over the years.
In 1945, when the Cubs last won the NL pennant, there was no NBA in existence yet, the NFL had at most ten teams (maybe nine, not sure) and the NHL had six. Major league baseball had a total of 16, eight in each league. So the vast majority of professional sports franchises now in existence couldn't possibly have challenged the Cubs for the distinction you mentioned, since they didn't even exist in 1945.
When you get into long-time professional sports records, here is quite an irony: the team with the most games won all-time is none other than the Chicago Cubs!