As far as I'm concerned, there are two IQs for travelers: Those who queue…and those who don't. If you plan ahead, you can avoid nearly every line that tourists suffer through (except for security checks).
Many museums are free one day a month—a great deal for locals. But for visitors, it's generally worth paying the entrance fee on a different day to avoid the hordes on a museum's free day. The Sistine Chapel feels more like the Sardine Chapel when it's open and free on the last Sunday of the month.
At popular sights, it can help to arrive early or go late. At St. Peter's Basilica at 7:00 a.m., it's heavenly to see Michelangelo's Pieta, free of the crowds vying for photos. Near closing time, I've been alone in Versailles' Hall of Mirrors, where kings and queens have preened.
Even at the most packed sights, there's often a strategy or shortcut that can break you out of the herd, whether it's a side entrance with a shorter wait, a guided tour that includes last-minute reservations, a better place in town to pick up your ticket, or a pass with line-skipping privileges.
At St. Mark's Basilica in Venice, you can either snake slowly through an endless line, or go instead to a nearby church to check a large bag—then walk right to the front of the basilica's line, show your bag-claim tag, and head on in (go figure).
Fortunately, many popular sights sell reserved tickets with entry times (often with a small booking fee that's well worth it). A reservation system helps blockbuster sights handle a huge volume of visitors efficiently by spreading the crowds throughout the day. For example, Granada's Alhambra in Spain smoothly admits nearly 8,000 visitors daily. Some sights even require reservations, such as the Reichstag in Berlin, Leonardo's Last Supper in Milan, and the Borghese Gallery in Rome.
Reservations are especially helpful at places popular with cruise excursions and big-bus tour groups, such as Germany's fairy-tale Neuschwanstein Castle. If you arrive without a reservation, you'll wait in line, find that tickets are sold out, or both. Those who've booked ahead can just show up at their reserved entry time and breeze right in. It's worth giving up some spontaneity in order to save time.
Some sights are notorious for grueling waits. These include the Eiffel Tower, Rome's Vatican Museum, Barcelona's Picasso Museum, and Florence's famous galleries—the Accademia (Michelangelo's David) and the Uffizi (the showcase for Italian Renaissance art). At these places, lines are completely avoidable by making advance reservations, usually online or sometimes also by phone. After learning how simple this is and seeing hundreds of annoyed tourists waiting in lines without a reservation, it's hard not to be amazed at their cluelessness. As soon as you're ready to commit to a certain date, book it.
Most tourist destinations offer a city-wide sightseeing pass (or "tourist card"), which includes free or discounted entrance to many or most sights—and sometimes covers public transit as well—for a certain amount of time (usually intervals of 24 hours). Do the math: Compare the price of the pass to the total of what you'd pay for individual admissions. Even if the cost is about the same, remember that time is money. These passes are almost always worthwhile if they allow you to bypass long admission lines.
Combo-tickets combine admission to a larger sight with entry to a lesser sight or two that few people would pay to see. The bad news: You have to pay for multiple sights to visit one. The good news: You can bypass the line at the congested sight by buying your ticket at a less-popular sister sight. You can wait up to an hour to get into Rome's Colosseum or Venice's Doge's Palace—or buy a combo-ticket (at another participating yet less-crowded site) and scoot inside.
Whether you have a combo-ticket or pass, never wait at the back of the line if there's any chance you can skip it. Don't be shy: March straight to the front and wave your pass or ticket. If you really do have to wait with everyone else, they'll let you know.
My bottom line about sightseeing in Europe: Be a smart traveler. If there's a line, there's usually a way to avoid it.