Most grasses prefer full-sun (8+ hours of sunlight a day), and some grasses can handle part-sun (4-6 hours of sunlight a day). But for areas that receive 2-4 hours a day, fine fescue is the best choice for northern climates. Unfortunately, if you have an area that receives less than 2 hours of sunlight a day you might need to consider a different type of groundcover.
For shady areas in the southern half of the United States your options are very limited. Warm-season grasses perform best in these southern areas, but warm-season grasses are also known for being intolerant of shade. Some varieties of zoysia can tolerant part-sun conditions, but the most shade-tolerant warm-season grass is St. Augustine (not available in seed form). St. Augustine grass has some drawbacks however, so be sure to do your homework before considering this type of lawn.