Rumi's comment above pretty much sums up the reality of the challenge very well.
However, acknowledging that you can't make an ideal experience for every single device, just like you can't make an ideal experience for every single person from every single background with every single need, you'll want to prioritize what to make the experience ideal for. Then, make the experience acceptable and as good as possible for everyone else.
Look at the purpose of your website and the possible uses. Why would someone want to view your site on a mobile device? What would they be hoping to do? How might that be different than what they'd do/expect from the desktop experience? There are several camps as to if and how you should give a degraded experience for mobile, and I won't get into those here.
Also, look at your website analytics. Are people actually trying to view your website on small devices? What pages are they going to? How small? What percentage of traffic is from tiny devices?
In my case, I'm working on a set of applications that integrate together. Mobile is a very important part of this, so even though only about 4% of traffic to the web-app component is from 320px (100dpi) devices, we make it work well for them. However, my longer-term plan is to optimize for down to 480px-ish devices while making things still work (with zooming) on the tiny resolutions. I know some people will disagree with this, but I feel it's better to give a great experience for the largest number of people instead of making sacrifices that affect everyone.
That probably doesn't give you the answer you're looking for, but hopefully it's enough to get you pointed in the direction that's right for your situation.