Q: Have there been any startups you've later regretted rejecting from YCombinator?
A: Sure, several. But I can't name names because it's not for me to disclose that they applied.
However, YC keeps track of the successful companies that they initially rejected and here are some of them of them that are known to have been rejected who have gone onto raise funding etc:
- http://sendgrid.com/ (went through TechStars and have raised a series B)
- CouchOne - http://www.couchbase.com/
- AfterTheDeadline - Acquired By Automattic
- Light Sail Energy - raised money from Khosla Ventures - http://lightsailenergy.com/
- SignPost - https://www.signpost.com/ - Raised $1MM off Google Ventures
- MyFit - Raised $1MM - http://www.myfit.com/
- Storenvy although they were kicked out of YC 
- Mark Zuckerberg's Sister Was Also Rejected To YC 
It's a two way street and sometimes the company may be happy they didn't get into YC because it opened different doors that led to success. Maybe in some cases YC could have closed some doors that were crucial.
Many companies don't even apply to YC because it's geared towards tech companies that do not require capital (and when they do eventually, it's for people, not physical resources).
I'm always happy to see people succeed, especially people I fired at one point. The beautiful thing about our field is that it isn't a zero sum game.
EDIT: none of the successful people I know spend time on regret
I wonder if YC already tracks this, maybe informally? It would be a good means of testing their own selection processes. Then again, they probably focus more on the "false positives" (YC startups that did poorly) than "false negatives" (the ones that got away).
Obviously they don't want to accept just anyone, that doesn't work for various signal, scale, attention and effectiveness reasons. They do however accept (positive) outliers without traditional credentials, which is the opposite of what a traditional company does. A traditional company is looking for safety, VCs and YC are looking for maximum leverage (not the typical financial two-fat-tails kind, the only-upsides kind that Nassim Taleb et al. likes).
As for your question, I can't imagine a reality where they don't track that sort of thing.
I rejected joining startup as a founding member or first hire, with at least one of them becoming a billion dollar company. I have no regrets, even for a second. You can't change the past, only the future.