The standard service plan is for the E to run express between Queens Plaza and 71st/Continental at all times except late nights. It is express toward Manhattan from approximately 5:30am to 11pm and from Manhattan from approximately 6:15am to 12am, 7 days a week.
The E also runs express during weekday daytime periods east of 71st/Continental (meaning that it skips 75th Avenue and Briarwood/Van Wyck Blvd). This is in effect from approximately 6am to 6pm toward Manhattan and 7:30am to 7:30pm from Manhattan. The E is local in this area at all other times (evenings, overnights, weekends).
Also, keep in mind that a handful of E trains begin/end at 179th Street during weekday rush hours (4 inbound during AM peak/outbound during PM peak and 3 inbound during PM peak as well). These trains run express from 179th, stopping only at Parsons Blvd and Kew Gardens/Union Turnpike before 71st/Continental.
All that being said, there has been a ton of track work on the Queens Blvd Line lately, leading to many varied service patterns on weekends and during overnight periods. These diversions can have the E running express or local on any segment during any time.
As for the A on Fulton Street in Brooklyn, it runs express between Euclid Avenue and Hoyt-Schermerhorn at all times except late nights. It is express toward Manhattan from approximately 6am to 10:30pm and from Manhattan from approximately 6am to 11pm, 7 days a week (Sunday morning express service starts later, at about 7:30am).
Just like the Queens Blvd Line, there has been significant track work on the Fulton Street Line recently, as well as on the 8th Avenue Line in Manhattan, which affects A and C service. This has resulted in many, many 2007 weekends where there is no C service and the A must run local.