Intarsia allows you to do absolutely anything you like with yarns and colors - virtually anything that can be charted can be done in intarsia. You can do intricate pictures, abstract art with hundreds of colors, a simple baby blanket with teddy bears and alphabets, or some traditional argyle socks. While stranded color knitting (where you carry two or more colors per row) does have some limitations on length of floats and numbers of colors you can use per row, intarsia (where you only carry one yarn at a time) is truly no-holds-barred fearless knitting.
So if it is so great why isn't intarsia more popular? Probably because of this:
In intarsia every single time you come to a color change, you twist the yarns (called an interlock) and start knitting with the new color. Therefore the old color just sits there at the back of the work. In the photo here (a simple intarsia sock pattern from Sweaterscapes) there are really only a few color changes but you can see the extent of the yarns tangling on the back.
There are three methods of dealing with all these yarns at the back of the work - yarn bobbins, yarn butterflies, or just cutting 2-3 yard lengths and leaving it all at the back of the work. The method you choose will be determined by which thing bothers you most - tangling yarns at the back of the work or dealing with even more yarn ends than are already created in intarsia. I use the third method because I hate tangling and I actually like dealing with ends.
I think another reason knitters shy away from intarsia is that it can require quite a few judgment calls. There are times when you might mix intarsia, stranded color knitting, and duplicate stitch in one project for a complex chart. There are also several ways to work in the millions of yarn ends so it is best to get some resources on the subject.
Kaffe Fassett is the king of intarsia knitting. He's written many books with many gorgeous and inspiring knitting projects. I own Glorious Color, Glorious Knits, and Kaffe Fassett's Pattern Library. While I think his amazing color sense matches Alice Starmore's his books do not talk much about technique. For technique I always recommend the little self-published book, Intarsia: A Workshop for Machine and Hand Knitting by Sherry and Keely Stuever of Sealed with a Kiss. It is quite inexpensive and available at Elann among other places. It has photos and diagrams and a sampler block and it also discusses duplicate stitch which can help quite a bit in intarsia knitting.
If you're interested in trying intarsia, I highly recommend grabbing the Stuever book and buying one of Kaffe Fassett's books (many are available used or remaindered in discount book stores). Sweaterscapes , Swakknit and NeedleBeetle offer some fun intarsia patterns. Finally, HERE is a free intarsia pillow pattern from Kaffe Fassett.