I've experienced mechanical incidents preventing or delaying takeoffs on:
Eastern 727 : 1987 Tuscon (don't remember)
Continental A300 : 1989 Newark (baggage door)
Continental 747 : 1993 London Gatwick (engine trouble)
Been on a Continental DC-10 and a Northwest DC-10 without incident.
I believe it is possible for some widebodies such as DC-10's and L-1011's and 767's to operate at LGA. I followed OAG for many years, and noted that although rare, it did happen on several occasions. LGA's problem is a combination of runway length and the fact that both runways are extended on piers making for some weight restrictions.
From the latest OAG directory: (http://www.oag.com/)
9:00a LGA 11:32a ATL DL 417 L10 0 2:32 Daily
Effective Oct 1
4:00p LGA 6:43p ATL DL 627 763 0 2:43 Daily
Effective Oct 1
So Delta still has some widebody flights (L-1011 and 767-300) scheduled to Atlanta from LGA.