I think you are confusing a few different concepts.
- aspect ratios
- pixel dimensions
- pixel density
For web pages, the aspect ratio isn't all that important. The variable is the browser width, of course. That's always been a variable and continues to be so. The typical solution is to design a fluid layout. There are various ways to handle that from the simple "body width=100%" to things like Responsive Design where the page layout will change based on various 'brackets' of page widths.
On mobile, the browser width is dictated by the pixel dimensions.
As for pixel density, there's two ways devices handle high density screens:
- they don't care
- they do care
Those that care are pretty much the iPhone. The iPhone 4 has twice the pixel density as the iPhone 3, but apple let's the iPhone 4 still think it has the pixels of the iPHone 3. In otherwords, you as the web designer/developer don't really have to worry about too much other than perhaps giving the iPhone 4 a secondary set of images that are twice the resolution if you want those users to see slightly 'crisper' images (they'll still be the same physical size on screen).
Those that don't care, don't care, and I typically suggest you not care, either, as users of said devices have become accustomed to the web as it is on their device already.
In terms of image/font stretching, that should never be an issue. You don't stretch type in HTML (or a least, shouldn't) and your images should typically be fixed width to begin with, so wouldn't stretch regardless of the screen size.