How can I disable cellular data on an Android device? Can I easily disable cellular data on an Android device and just use Wi-Fi? Does this change based on whether or not I have root on the device?
You can pretty easily disable cellular data on an android device without root.  On Android 2.2 and above, you can go to home --> menu --> Settings --> Wireless &amp; networks --> Mobile networks --> and then uncheck Data enabled (on phones with Motoblur, the Data enabled setting might be in home --> menu --> Settings --> Data manager --> Data Delivery instead; YMMV).

If you have Android 2.1 or less, or just want a widget that will let you turn mobile data on and off, there are several apps that do the trick, for example Widgetsoid and APNdroid.
Like Matthew Read said, the major carriers won't let you put a smartphone on their network without a data plan.  However, you might have better luck with smaller carriers that operate on the big carriers' networks.  You end up getting better prices but the same coverage areas.  For example, Walmart Family Mobile plans include unlimited talk and text, and pay-as-you-go for data.  So if you don't use any data, you don't pay for data.  They run on T-Mobile's network, and you can either buy one of their phones, use a T-Mobile phone, or an unlocked GSM phone.  Here are a few other examples:


Boost Mobile (Sprint)
Simple Mobile (T-Mobile)
Virgin Mobile (Sprint)


And then you've got other carriers that operate their own smaller networks, but have roaming deals with the bigger carriers, so once again you still get coverage areas comparable to the major carriers:


Cricket Wireless
MetroPCS
US Cellular


There's a more comprehensive list of US wireless companies that operate on the larger companies' networks here:

http://en.wikipedia.org/wiki/List_of_US_MVNO