So, one of the companies I'm in is not going to file its 10-K on time, and is potentially going to get delisted. Hence my "sudden" interest in this topic =)
To summarize, for the NYSE, a company gets a grace period of 9 months from the deadline, after which NYSE will determine whether or not to let the ticker to continue to trade (up to a period of 3 months more). For the NASDAQ, there is no such grace period.
See http://www.thecorporatecounsel.net/blog/archive/000621.html and http://www.sec.gov/rules/sro/nyse/34-51777.pdf for more information on the NYSE and NASDAQ stance on delisting for late filing of 10-Ks.
From my readings, my impression is that a company is able to officially request for an extension to the filing deadline, for both NYSE and NASDAQ, despite the fact for example that NASDAQ does not have a grace period.