No formal birthday recognition from United, but about 6 years ago I was caught up in the big messy nor-easter of whatever year it was, had to evening flight out of BWI cancelled after boarding. Next day I'm at IAD, which is re-enacting the Fall of Saigon (never, ever, been so appreciative of lowly 2P status, which enabled me to use Premier lines with a 10-minute wait instead of GM line which literally ran the length of the building!!!). Re-routed IAD-SEA-SFO. Fight to SEA
delayed enough to miss my SFO connection by 15 minutes. Last flight to SFO.

As we're landing I do my usual thing, looking to see my connection pulling away from the gate. Instead an FA approaches me and says, if I run, I can make my flight.

I get off the plane and there were literally four UA staff pointing where to go and waving me through. The people on the plane to SFO must have thought I was a VIP to have the plane held! (I'll admit I was in F). And yes, it was my birthday, but no mention of that was ever made. Sure was nice though.