I made a website that adjusts to different screen sizes, and I think it looks like shi*. It looks good in a browser window (at about 980px etc), but it changes and everything gets smaller when I make the window smaller. I guess the best way to go would be to make it fixed width on PC / iPads / Laptops and make it use different css for iPhones.
Responsive designs can be great if you take the time to make multiple style sheets to adjust for different screen sizes, thus allowing you to hide elements and adjust font sizes appropriately. A good site for testing pages is Responsive Web Design Testing Tool [mattkersley.com] allowing you to see five screen sizes simultaneously.
My argument against responsive designs has to do with bandwidth. I rather a separate "mobile friendly" version so a user can choose. No sense having them download a bunch of elements that they cannot use or see. And even though I have done a few responsive designs, I find it faster to do a mobile friendly version. And even though Google says "responsive designs are preferred," I find it funny they use two separate versions. Do as I say, not as I do.
You need to do more than adjust the font size for responsive design or even for a separate site. If your site looks good at 980px, the same content will never look good in a typical 320 px mobile window.
You need to remove some elements completely and revamp the remaining ones. If the site wasn't designed with responsive design in mind then you'll be lucky to get away with just using css - a redesign will probably be required.
And I agree with marshall, forget responsive design on existing sites. I have used a separate site for my mobile version, I can't have all the complexity of reformatting a site with an old design to display well on pcs, mobiles and tablets. And yes, G recommend responsive design but many major sites have chosen the separate mobile site (or subdomain) route and G picks them up fine.
A brand new site is a different proposition though. I would model it with responsive design in mind.