One reason to make your own butter is that you get distinctly different flavours depending on the type of cream you use.
If you use fresh cream you get sweet butter which is popular in North America, Australia and Britain, but less easy to come by in continental Europe. If you use a cultured cream like Crème fraîche you get cultured butter, which is common throughout most of Europe.
Cultured butter is slightly soured by lactic acid. It has a fuller, more complex flavour than sweet butter. If you decide to make it, be sure that you don't use a cultured cream that includes artificial thickeners. The ingredient list should read something like "pasteurised cream, lactic-acid culture" (apologies if that's not accurate; I'm translating from Swedish).
I have a couple of other reasons why I personally want to make butter. First of all my four year old son has been asking how butter is made, and this would be a great way show him. The second reason is that I'm curious as to how real buttermilk tastes (the buttermilk in the supermarkets is fermented milk). And last of all, I noticed that my beurre noir sauce was working out much better when I lived in Australia, so I'd like to do some side-by-side comparisons with European butter.