Just curious, and if so, for what type of ship, etc?
It all depends on what you want to do. Are you doing PVP, running STFs, just having fun? What kind of ship do you fly and how do you like to play? Are you a tactical, engineer, or science? We need details!
For the most part if you're just playing missions and doing non-STF, non-PVP stuff you'll be fine running almost anything you want, mines included, but since you're here we can only assume you want more substantive advice than that. For that we need more details.
Personally I used mines all the way up until I started running STFs, just because they were fun and I liked seeing all of them explode together after hitting dispersal pattern beta.
I stopped when I switched to an escort with 3 turrets in the back. Now that I'm trying out a cruiser I'm seeing if they're a worthy alternative to a rear torpedo launcher or beam.
Now that mines have been buffed they're a much more worthy choice than they used to be, but again, whether or not you can be competitive with them tends to depend on how you play.
Okay in there you see a cruiser that is just so darn fast it can whip around and cycle a fore and aft torpedo and keep full time beam array fire going. That's a commander level ship in STF. So any time that you may wish to use a mine, you could just use that aft launcher. Say I wanted the aft launcher to be Chronitons for slowing probes? Easily done on a fast ship like that and the range on the torpedoes is an obvious plus.
On a slower ship using limited arc weapons you wouldn't want to do that. You would be keeping your ship in the path of the probes or in the case of the larger gates or stations you would be within mine range. On those ships you're just replacing a turret for a mine. A very easy trade to make.