Will you use your mug on the road? Car commuters need a mug that fits in their car's cup holders. It should fit snugly enough that it can't rattle around and possibly tip over, but not so snugly that you can't get it out easily for a sip. Check the size of your car's cup holders and compare it to the base of the mug, and if there's a handle, make sure it doesn't get in the way. Also, hold up the mug to your face to make sure the open lid won't obstruct your view as you drive.
Do you want to reheat your mug in the microwave? Stainless steel isn't microwave-safe, so you'll need a plastic mug for microwave use, or else one of the rare travel mugs that's made of glass or ceramic. However, not all plastic mugs are microwave-safe, so you should check all the instructions and labels before you buy. Also, keep in mind that a double-walled stainless-steel mug will do a much better job of keeping your drink hot from the get-go than plastic or glass, so you might not actually need to reheat it.
Are you picky about flavor? One problem with plastic mugs is that they're more likely than stainless steel to give your drink an off-taste, or to retain odors and tastes from previous uses – even after a good washing. However, for those with extra-sharp palates, even a stainless-steel mug can affect the flavor of its contents. A stainless mug lined with glass or ceramic solves this problem, but it's also more prone to breakage than a regular stainless mug. A newer option is stainless steel with an electro-polished interior (such as Zojirushi's SlickSteel finish), which is less likely to hold on to flavors or odors. True coffee snobs may wish to pour their coffee out into an open ceramic mug before drinking anyway, since this is the best way to get the full aroma of the coffee as you sip it.
No matter how well your travel mug insulates, it can't change the laws of physics. If you pour a hot or cold drink directly into a room-temperature mug, it will begin to change temperature immediately as heat transfers from or to the surface of the mug itself. So if you want to keep your drink hot or cold as long as possible, give your mug a hand by filling it with hot or cold water about 10 minutes before adding your beverage.
To avoid damaging your mug, follow the manufacturer's cleaning instructions closely. If the manufacturer says the mug shouldn't go in the dishwasher, pay attention; the heat of the machine could damage the mug's vacuum seal. If your mug needs to be washed by hand, take the lid apart so that you can clean all the parts carefully and clear away any lingering odors. A good bottle brush can help with this job. Testers at TheSweethome.com recommend the OXO Good Grips Water Bottle Cleaning Set (Est. $10), which includes a long bottle brush, a detail brush for cleaning the lid, and a narrow brush for cleaning a straw attachment. If your mug has silicone seals, you may find that they pick up odors over time; burying them in baking soda for a couple of days should take care of the problem.