In past decades, Internet Service Providers would sell DSL service with the requirement that you also purchase phone service. One service was linked to the other, and you were required to buy phone service if you wanted DSL.
Nowadays, ISPs usually do not have that requirement. You may now buy “Naked DSL” from your ISP and abstain from paying for traditional phone service.
Specifically, I can mention that a local ISP (Shentel) started offering Naked DSL in October 2015. They sent out a letter about it, but it was worded in a confusing and discouraging format. So this is your heads-up: Shentel customers do not need telephone service in order to have DSL internet service. You may discontinue your landline number, save some $$$ and still keep your DSL!
If you have DSL internet service with another provider, you can always contact their customer service folks to ask if they, too, allow for Naked DSL. Although, not everybody is comfy with that term, so you might instead call it Standalone DSL or “DSL without landline phone service.”