Is this possible at Verizon?
It is possible, but few and far between does it happen. There is a list, including the Motorola Q, that will work without data. The rest, especially newer ones, require a data plan.
Current device: White 16GB Samsung Galaxy SIII
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The are a few reasons to want a smartphone, the ability to use apps, better calendar functions, superior browser experience, easily able to sync your phone to your computer, WiFi. Almost every coffee shop and a bunch of other places I frequent have WiFi so I could browse the web and check email there.
Here's the answer most people don't like, Verizon won't allow you to have a smartphone without a data plan unless you get something really old that isn't really a smartphone but rather a combination of a PDA and phone. They make an exception on phones like the old Moto Q because you only have 1x data and would likely be hard pressed to use 20mb/mo.
What you can do is get a Verizon branded phone, but you would either have to pay full retail for the phone or find it on eBay, Craig's list, or replaceyourcell.com. I know there are a couple others and somethimes you can get a cheap phone on Amazon.com without a contract, google palm pixi plus, as they can be had for under $50 shipped with no contract. Now you find a place like Page Plus Cellular to activate your phone, this is a little more complicated because you don't get the hand holding like you do from Verizon, you have to be able to do a little research and figure things out yourself. In this case you can find a Droid Incredible or something online, the Droid Eris can be had cheap, then you can put a $30 pin on the phone for 1,200 minutes, 3,000 text and 100mb of data plus you can turn data off and just use WiFi. The Pixi Plus is rather small for some people, but it's a cheap and easy phone to use for someone who doesn't need top end. With PPC you have the choice between 2 monthly plans and several standard plans were you just add minutes good for 120 days and what you do comes out of the pin you just purchased for your phone, no add on data required. Just FYI, while you have a Verizon branded phone, your friends won't get m2m when they call from their Verizon phones, so something to consider.
Go on prepaid with a mvno like pageplus
Home ISP, RR-Ultimate WiFi, $90/mo | Verizon 4G, $30/mo Unlimited
School, $5,000/semester | Work
buy an ipod touch or a portable android device.
next time use the search button.
I've seen 7" android tablets for $150, not a really bad deal. More places are getting free WiFi all the time, so it's something I've been thinking about as well.