I replaced the stem (because the 2008 one is HEAVY) but assuming you get the 2009 one, it hasn't got a stem. I also did the handlebars (because I like them flat and because it wasn't compatible with a standard stem). This was an inexpensive thing to do; stems and bars can be had for $10 or even less each if you look out for good prices.
I put on Ergon grips; these are pricey though. Ones from BBB (called Ergo) are much cheaper and give the same comfort. Some neato small bar ends will give additional hand positions.
I installed Big Apples (from Thor) but ran the original tyres for quite a while. Nothing wrong with them except a but slower, but the Mini won't break speed records anyway. (To be sure, I set my record of 74km/h on the original tyres.)
I got some really inexpensive 16" mudguards (fenders in the US) from a local ebayer. The front is fixed with just the fork fixing, I didn't install the stays as it is hardly necessary for such a dinky guard. The rear was easy to install with just the front fixing point and the stays. I elected not to put in a 3rd fixing point, again it is hardly necessary. I did move the stays so that they are closer to the top of the mudguard instead of near the back.
Of course IMHO the most important mod is the Nirvana suspension mod - replacing the spring with a rubber cylinder. Bruce Metras came up with this idea first by installing a Birdy elastomer on his Mini. I used a rubber doorstop.