They work really well with stealth characters, try setting up some choke points in interior cells and remember to stack them up nice and thick...
One of the best missions for mines is Boston Public Library. I try and save up about 25 of them and then spread them all over the building before the mutants start arriving. The resulting fireworks will usually tag most of the mutants as they come in so even if the robots kill them you'll still get the EXP.
Great for snipers as well, if you're taking on a big base of enemies you can set a bunch of mines around your camping position in advance.
Mines are just huge fun!
Weird...I never seem to have enough mines for what I want to do. I seem to use them not before combat, but during it, especially if I'm fighting a melee-heavy faction like raiders or super mutants. Often I will get to my perch before combat and lay mines as I go, knowing that the raiders armed (sadly) with only a pool cue will run into them. Often the ten or so I've laid down are enough to down at least a few.
I do sneak around a lot, but at this point I basically get really close and headshot them, or do it from a moderate distance. I guess I can think of several situations where I can use them, but I alway feel like I can do it quicker and easier with my guns. Even on Survival it's really easy for me to kill things, especially since I have a near infinite amount of most supplies. I'm hoping the survival update will make it it harder, because right now I don't even really use Stimpaks much. I have 1000+ of them in a wooden cabinet in Sanctuary, in addition to a mountain of ammo and a few hundred frag grenades (which I also don't use). I really should just max out my explosives perk and just go out with a large amount of mines and grenades (nothing else) and see what happens.