While federal communications regulators have been writing rules of the road for how broadband providers can treat traffic on wired networks, wireless providers have been building private little speedways.

The new, low-cost wireless plans with unlimited access to certain apps that don't count against a user's data limit are adding a new dimension to the net neutrality debate. Wireless carriers say the plans are a cheap way for people to keep in touch with friends and family. One plan, for example, gives users full access to...