So, you're building a new website. And you don't want to just throw your money away, so you'd like your shiny new website to last, what, about 5 years? That sounds reasonable. (Most 5-year-old websites that I've seen are starting to show their age.)
An important question for you, then, is what will the market look like between now and five years from now? What do you need to keep in mind when you build your new website?
If you're concentrating on a building the most awesome, beautiful desktop site right now, and mobile is only a second-class consideration to you, your site will be woefully out of date in five years. Mobile is the future.
Consider this: more and more people are buying smartphones. In fact, Horace Deidu predicts that between 2015 and 2020, smartphone ownership will reach 90% saturation, much like the car, the radio, and the color TV (but never the PC). Couple that with the fact that, in the past 6 or 7 years, the number of smartphones and tablets sold has nearly caught up with the number of PCs ever sold. (Oh the last graph on that page is good.)
Pretty soon, almost everybody will have a smartphone. And typically, that smartphone is with them at all times. Regardless of what you feel about people's context when using that smartphone, "almost everybody" is not a demographic you want to ignore.
If mobile is not a big part of your five-year plan, it may be time for a rethink.