If you really want to feel like a freak in Venice, walk around without a cell phone. Italy has among the highest cell penetration and the cheapest airtime in the world. You'll even see gondoliers yacking on their telefonini with passengers on board.
Truth is, I've never had a cell in Venice, and it's caused many a logistical inelegance, not to mention the sting of the stigma of being off the grid in a place where Nokia and Ericsson are as well known as Tintoretto and Titian.
I took some "high powered" hand-held radio tranceivers with me a few years back, and instead of the promised "one mile range" I wasn't able to get a clear signal from one end of the Piazza to the other. Plus I looked like a dork. Over.
I'm supposedly a consumer technology expert, so I figured I needed to crack this cipher before going back to Venice in July. Solution: For under $60, shipped, I snagged two used Motorola V66 cellphones on Ebay. Nothing exciting ... slim, flip-open, mono-screen. But they are tri-band GSM babies, which means I can pop in a TIM or Vodaphone SIM card - available for purchase everywhere in Venice - and go. Many if not most Italians use the same pay-as-you-go method.
(By the way, there are many phones available here that work overseas ... you want a GSM compatible model that uses the 900/1800/1900 Mhz frequencies ... just do a little research, it's easy.)
There are rental places on the net, but they are ripoffs. They charge more for a two week rental for one phone than it cost me to buy two. And they totally hose you on the airtime/SIM cards. So brew your own. Ebay sticks it to the man once again.