Definitely look at the Fastpass to see what time it says you can get your next Fastpass. When we were in Epcot on our recent trip, I ran over to Test Track to get Fastpasses for DH and DS while everyone else in the family hung out in the shade -- the Fastpass for TT wasn't good ffor 3 hours but stated I could get another Fastpass right away, so I ran over and snagged Fastpasses for The Land and Soarin'. We grabbed lunch and then were able to use the fastpasses for The Land, Soarin', and Test Track (in that order) with minimal waits.
At MK, on the same trip, I snagged Fastpasses for Philharmagic just as we were getting in line for Dumbo. By the time we were done riding Dumbo, it was time for our return to Philharmagic. But before going in Philharmagic, I jumped over and grabbed Fastpasses for Peter Pan. By the time we were out of Philharmagic, we were able to go right over to Peter Pan. We did 3 attractions, but only waited in one line.
You can do a lot using the Fastpass system for the attractions nearest to you, but if you are running across the park to get tickets for just one or two rides, then send one member of your family with all of the tickets -- it's much easier and faster for one person to jog across the park than it is to drag the entire family.