Do you even have one? Mine is R2-D2 which sits next to Wall-E in a relatively small mug collection.
This is my mug. http://imgur.com/vsSM0X0 I like the minimalist/zen feel. It's not too big and not too small. It's also the perfect thickness, so it disperses heat at just the rate I like. A good, no-nonsense, functional mug. 9/10
Mine is a plain red one with #banging written across it. Banging, in this case, being intended to mean as it does in the top definition here. Ironically, of course - what do you take me for? Which was fine, until my Mum saw it and interpreted it rather differently - as per the second definition in the link above. She's still puzzled as to why I'd have a mug celebrating the raw fact of sex, and probably now thinks I am overcompensating...
My girlfriend recently bought me a great mug. It says "Despite all my rage I'm still just Nicholas Cage" Nick Cage is (oddly enough) an important part of our relationship, so it's really nice to have a mug that reminds me of his amazing acting career. Plus it's a massive mug, and the only one I've ever found that actually fits my hand.
It's a wonderful mug even without the text. Fits like, two to three cups of coffee (my morning blend now is two cups of coffee, two shots of espresso, and some milk). The handle fits all four of my fingers, which never happens with normal sized mugs. All in all I 100% endorse it.
I love my Aperture Science mug, which I haven't found since I moved. :( Right now the one that's getting the most use is the one I got for backing the Reading Rainbow Kickstarter because it's either that or the boring mugs that came with our dishes.
There's personal value intrinsic to objects you have had a part in creating, I think having something truly unique in the world is fantastic and I am hoping to incorporate this into my lessons when I start teaching. Students build websites and such already but I've not seen any really take ownership of their creations, perhaps this is a value only for physical objects? Perhaps 3D printers can change this? I have a few photo mugs but I've never tried designing my own, but now I very much want to.
I actually used an online photo printing service offering 25 free prints so I printed out screenshots from Star Wars Galaxies so I could remember the time I had with my friends. I had completely forgotten that until now. I've never been one to keep digital cruft for too long, every so often deciding "I have nothing of worth on here, just reformat it all" and it's only some time after I realise what was lost. As you said, it can all be deleted with one click, so ownership (and pride) of things digital can be fleeting: a mixed blessing.
I couldn't name the sites I used to visit, but there is one that I ran. I built a forum for my Star Wars Galaxies guild to use, that was probably were I spent all my time: discussing the game, our lives, the news, and the future. That friend group developed really well both in and out of the game. We later tried migrating over to Star Trek Online but the game never lived up to the designs they were telling us of (I think another company took over?). We'd filled this forum with long discussions of what we wanted, how we thought it would be, and had lived futuristic adventures vicariously through text and our imagination, all for it to be lost as we turned away and moved on with our lives. I don't think I could put my feelings on that past on to a mug; it seems silly but when it was such a huge part of my life at the time it hurt to have it end with such a... fizzle.
My favorite mug has the quote "just when the caterpillar thought the world was over, it became a butterfly..." colorfully printed on it. That's cute and all, but I remember that what stood out to me the most about it was the texture (it has this interesting matte-like finish) and the large handle size. Found it brand new and still boxed at a garage sale for a dollar.
http://www.ikea.com/us/en/catalog/products/70258911/ Simple. Durable. Stacking. Reasonably sized. Cheap. Ticks all my boxes.
The smallness is a bonus for me. The frequent trips to the pot forces me to confront the depth of my coffee problem. I actually like the handle, in so far as it doesn't get in my way. I've never seen the point in mug handles. If it's too hot to cup in my hand, its too hot to drink.
To me, the material and form is more important. I am a very picky drinker and can't stand drinking a hot beverage from a glass or thick ceramic mug. I have a Limoges porcelain mug that has the perfect thickness and weight. I use it to drink tea with milk.
I have two. The first is a mug from the Charlie Rose show that was left behind by a college roommate when she moved out of our apartment for the summer. I just got it back after not seeing it for 8 years when my mother brought me several boxes of stuff I left in her attic. I don't know why, but I seriously love this mug so much. The second is THE best one, it has Data from Star Trek: TNG. He is a simple light grey line drawing standing on a transporter. I'm pretty sure at some point he must have disappeared when hot beverages were put into it, but I imagine it's pretty old so it doesn't work. On the other side is a fake Brent Spiner signature. I found it at a thrift store and was so psyched that I yelled "YES", because I had been looking for a good Data mug on the internet for a very long time. I also have this really great little demitasse that isn't particularly special, but it's the perfect size and I really love it. I have had a lot of very special coffee mugs, but this is my current collection.
My girlfriend got me this one mug with a banana on it that said "There's always money in the banana stand." Which is an Arrested Development reference for those who don't know. I love that thing. I think she went on one of those sites where you can design one yourself so I don't think I can link a picture of it sadly.
Well then it is my favorite, I drink the fuck out of some water with that guy. I also hold it weird as I pound the water, I put my hand through the handle with my palm facing the outside away from the main cylinder, then I rest the main cylinder on the top of my wrist. Then I pound that water, pound it hard. I would not be able to pound that water so hard with out my Maß mug.