Doug spreading mis-information yet again...complete hog-wash. There are oodles of coins post-1964 slabbed in the 1990s by NGC. For example, the example @Conder101 gives as his example in his slab variety history of NGC 5.0 (used c. 1992 to 1995) is a 1974 Ike Dollar (see below).
Chris, NGC added the USA "Modern" tier to their submission forms on June 1, 2002. That encompassed coins from 1955 to present. I'm not sure where Doug got his information of 2001 being some sort of cut-off for modern submissions... Well before NGC added their "Modern" submission tier they were accepting modern coins for grading and encapsulation. I can't find an exact date, but it was at least the mid-1990s.
OK, I found a thread on the NGC site with a reply from David Lange. He said that "It was around 1995 that NGC began to grade coins dated 1965 and later." Now if that's not a piece of information straight from the horse's mouth, then I don't know what is. Cheers.