Don't go on a Saturday! If you must go on a weekend, go on Sunday. I can't emphasize enough that on Sunday the crowds will be nothing until around 1:00 PM, but on Saturday it will be crowded from start to finish. The attendance of a normal day is doubled or tripled on any Saturday. Sundays are much better since they have 1/2 the Saturday crowds (20,000 fewer people in lines) and weekdays are even less.
The park is open for weekends only starting on March 1, and daily operation is in place April 5-14 and from May 23 through August 10. The last operating day for 2008 will be Sunday, November 2.
The only reason to go on a Saturday is if
you can brave bad weather. If it's drizzling, or even raining,
the coasters will still run (except for MindBender) and
you can have a good time. But the "sane" people will
all stay home. The best kind of weather is if skies threaten but
never amount to much. The other Saturdays are the first few weekends of March before most people know the park's actually open.
On a 3-day holiday weekend, Monday is usually the day to go as Sunday becomes almost as crowded as a Saturday in the afternoon. But a holiday is a tough call as to which day will be less crowded.
If you aren't interested in a concert I also recommend avoiding concert days (unless you just want to stop in late in the day when everyone else is attending the concert). And definitely avoid the ending weekends of both July and August since most of the free ticket offers expire then. Other than the discounts expiring, the first weekend of October has always been a great time to go and ride the rides. This is a dead weekend between the normal shows and Frightfest shows, while all the shows are closed the rides are open.
The best times to go are early spring weekends, Spring Break weekdays, the last weekday operations in August (not the weekend), and the Friday nights during October's Frightfest. Note that SFOG is open WEEKENDS ONLY from March to May (excluding Spring Break) and also from mid-August to November, corresponding with the Atlanta area's school schedule.
The best days during a normal operating week are usually Tuesday and Thursday.
"Pearl Day" (known by many as "Gay Day") is the Wednesday before Gay Pride weekend (note that this event is not sponsored by the park).
Depending on what you want to do (or not do) you should also check out any special events that may be happening on the day of your planned visit.