At most times of day you'll see a line of people snaking around the Uffizi. They're waiting to buy tickets, and you don't want to be one of them. Instead, call ahead for a reservation (055/294883; reservationists speak English). You'll be given a reservation number and a time of admission—the sooner you call, the more time slots you'll have to choose from. Go to the museum's reservation door at the appointed hour, give the clerk your number, pick up your ticket, and go inside. You'll pay €4 for this privilege, but it's money well spent. You can also book tickets online through the website www.polomuseale.firenze.it;the booking process takes some patience, but it works.
Use the same reservation service to book tickets for the Galleria dell'Accademia, where lines rival those of the Uffizi. (Reservations can also be made for the Palazzo Pitti, the Bargello, and several other sights, but they usually aren't needed—although, lately, in summer, lines can be long at Palazzo Pitti.) An alternative strategy is to check with your hotel—many will handle reservations.