Over the past 6 years while living in Minneapolis, the vast majority of my riding has been on a single speed (road, mtb, and cross).
My rolling 16 mile ride in to work is ideal for single speed use. With the gearing I run, (48 x 17) I roll along at a steady pace, but am comfortable pushing the gear up most climbs and can spin the gear out at high speed going down a hill or keeping up with auto traffic. My bike of choice for city commuting is the Salsa Casseroll Single Speed as pictured to the right.
Additionally, I've ridden Mountain Bike all over the US as a single speed with success. From Wisconsin to Colorado, Minnesota to Utah, it's all doable. Just pick the right gear!
In selecting a gear, consider how fast you will be riding on average over a particular course. Also, what your top speed and lowest speed will be. Also consider that riding slower than 3 or 4 mph, walking is just as fast and will likely be more efficient. If you are looking for a comfortable gear to pedal, underestimate your average speed and vice-versa if you're a tough guy or gal.
Now go HERE to the Sheldon Brown Gear Calculator. This is a nifty tool that I've used for years. Change the "Gear Unit" field to your normal pedaling cadence (mine is 90). Now try plugging in various chain ring sizes (into the "chainrings" field) and rear cog/freewheel sizes (into the "custom casette" field). You'll eventually find a chainring and cog/freewheel combination that works for you. Realize freewheels and single speed cogs are generally no smaller than 15 teeth an no larger than 22 teeth or so. There are however many chain ring options available for most crank arm sets.
Once most cyclists get a taste of single speeding, they can't get enough. The simplicity of a single speed is beautiful! Silently riding along on a single speed or fixie is like nothing else! I also find riding a single speed great training for racing!
From a training perspective, consider riding a slightly bigger gear than you are comfortable with. It will force you to push the big gear on the ups as well as encourage you to go faster in general, such that you can spin a comfortable cadence. Several friends of CyclovaXC train almost exclusively for the Chequamegon Fat Tire Festival almost exclusively and are always ready to rock up there!
Get on your bike and ride!