We've already mentioned the Basilica di San Marco, but there are scores of other churches in Venice that are worth your time. Some have modest admission fees (you can save money with the Chorus Pass), but some are free.
The largest and most famous of the no-admission churches is another basilica: Santa Maria della Salute (shown above and at right), which is near the mouth of the Grand Canal and the Dogana di Mare (Venice's old customs house) at the tip of Dorsoduro. The massive eight-sided church sits on more than 100,000 wooden pilings. It was completed in 1681 as a "thank you" gift to God and the Virgin Mary for allowing the plague to kill only a third of the city's residents. Admission is free between 9 a.m to noon and 3 to 5:30 p.m., but there's a small charge to visit the sacristy.
A few smaller churches, such as the Carmini church--also known as Santa Maria del Carmelo--are also free. (The Carmini church is on its own square near the Campo Santa Margherita. It shouldn't be confused with the Scuola Grande dei Carmini, which is nearby.)
On the island of Murano, you can enter San Pietro Martire (inset photo) free of charge, but there's a small admission fee at the more interesting Basilica dei Santi Maria e Donato.
At other churches, admission may be free out of season, when there aren't enough visitors to justify having a ticket vendor on duty. (We wandered into the Gesuati church on a weekend in November, and there was nobody around to collect the admission fee.) Admission is also free during religious services, but you'll be expected to grab a spot in a pew and worship instead of wandering around with a guidebook in hand.
Santa Maria della Salute Church on our main site
Venice Chorus Pass on our main site
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