Great question! As with many great questions, the answer is "it depends".
Industry standard says you should allow 30" per adult in a formal dining situation for square or rectangle tables. This would mean a 72" Long X 48" Wide table would seat only 2 persons on each side and one person on each end. For holiday gatherings and/or family dinner, 24" per person is usually sufficient. Be aware of the width of your chairs, though, as chairs with arms may dictate the number of guests you seat more than your table's size. Using the family dining rule, a 72"L X 48"W table could seat 3 individuals on each side and as many as 2 on each end for a total of 10. Your chairs and your guests will determine the right amount of space to allow in your home. Tables of less than 48" in width will only seat one adult per end. Oval tables will also only seat one guest per end.
Round tables measure differently. A 60" diameter table typically seats 8 adults. 72" rounds will seat 10 and you gain 2 diners per 12" as sizes increase. Again, arm chairs may intrude on your space a bit, so take a practice run of just table and chairs before attempting to seat your guests.