Everyone, no matter how many mugs they may have, invariably finds themselves coming to favor one or two over all the rest. At first there may seem to be no rhyme or reason to it, yet there are certain characteristics I believe distinguish great mugs from the merely serviceable that are almost universal.
One of the best places to get really top-notch mugs by the way, are those little gift shops you find in art museums and high-end botanical gardens (which I have written about at greater length here). The only downside is that mugs there are never sold in sets, only as separates, and they are ruinously, even comically expensive. My own best mug has a charming strawberry print, is of a pleasing thickness, and probably cost upwards of twenty dollars. This is an insane amount of money to spend on a single coffee mug, but I love it with all my heart and want it buried with me when I die.
The ideal mug should be neither too large nor too small (adjusted for American sizes; I like the coffee in Australia and New Zealand, for example, but it's not nearly enough. The biggest coffees they've got are like 4 ounces! While I don't wish to change how they go about their own lives, that leaves me with too much morning. I can't make that coffee last longer than 5 minutes, and then what am I supposed to do with all that leftover morning?
Squatness and the golden ratio
A really ideal mug should be reasonably squat, although – and this is critical – never so squat that it becomes as wide as it is tall. Certainly not wider than it is tall. A mug that is wider than it is tall pretty much guarantees your drink is going to be lukewarm by the time you reach the midway point, at which point the entire morning has to be scrapped and you have to wait until tomorrow to start the day over again. A little boxy, that's what we're looking for, not a perfect square.
Too thin and the mug radiates heat; I have a horror of mugs that lose heat due to the insufficiently-insulating thinness of their sides, like how fathers in old cartoons and books are always complaining about leaving the door open while the A/C is running: I'm not trying to warm up the whole kitchen here. I'm trying to warm up this one drink. Besides, if the walls of the mug are too thick, you're liable to burn your fingers the first time you try to pick it up. You want your hands no more than pleasantly warmed by the mug. Too thick, of course, and the lip of the mug becomes unpleasant against the mouth; it is possible to overcorrect here.
Alternately, one or two of those insulated Thermos-style mugs, with metal sides and no handle, are pretty good to have on hand for when you want to nurse a cup of coffee over the course of an hour or so but don't want to go to all the trouble of reheating it in the microwave every fifteen minutes. They'll never be a best-ever mug, but they are undoubtedly useful.
White or off-white interior
The best mugs have a white, or a very nearly-white interior so you can clearly see how strong the tea is getting before you put milk in, or update in real-time the amount of grounds you've got in the filter in case the coffee is too weak. Several of my third-best mugs could be second-best mugs if it weren't for granite or amber interiors.
Exterior can be whatever
I don't know, maybe you like yours highly decorated, or diner-style-plain. It's up to you!
A straight lip is best. It can be slightly curved outwards, but only slightly, otherwise you risk dribbling. Straight walls are best too, I don't like those mugs that bulge out around the bottom, like a rococo candlestick. It's a vessel, not a fountain. The bulgey ones are good enough for evening guests being served a cup of tea before they go home for the night, which spares your special mug for your own cup of coffee the next morning.