Is responsive web design a must....no
Is mobile friendly web design a must.... yes
why the separation you may ask, because you don't need to do a responsive website to embrace mobile browsers, you can do separate style sheets for mobile, print and desktop, you can do responsive and you can also do a mobile site or a mobile app. There might be some other options too but ultimately you have choices, which is best really depends on the site.
Personally I'm trying to embrace responsive web design, html5 (flash is only going to be used for video fall back) and css3 with my new site that I'm working on, it's still not as 'efficient' as it could be because a lot of the browsers still require us to use moz or webkit versions of the css3 standards because, some haven't been ratified not to mention ie's shortcomings. Then there's the fact there is no 'retina' standard meaning you need to use media queries or a script to cover 'high res' images.
Do I think it's worth it, probably in the long run, I just wish they'd hurry up and standardise the damn thing lol.