Depends on the coin dungeon. Keep in mind that the coin dungeons rotate out every couple of weeks, too, so the descriptions I give now aren't going to be valid soon. :P
[top]Dragon in Motley
Dragon in Motley is kinda meh. It's an easy dungeon, which is good, but Jester Dragon, Drawn Joker is very situational in his usefulness. His stats are on the low side (except for RCV, which is remarkably high for a Dragon/Devil) and his leader skill is only useful in specific dungeons. He is, however, the only monster that packs Guard Stance - Dark, which could warrant his inclusion on an appropriate team.
[top]Sword of Flames
Sword of Flames is worth running -- it drops Burning Phoenix Knight, Homura. His stats aren't end-game caliber, but they're still solid. He still finds a place on my fire team. His active skill is good (water orbs -> fire), his leader skill is useful on the right team (2xATK/RCV to Balanced), and he's packing Two-Pronged Attack which augments his decent-but-not-great ATK. (It's a bit annoying to level up additional copies for the awakenings... I used Tamadras.)
[top]Pirate Dragons
The pirate dragons are... eh. They've got moderately good stats (by modern endgame standards, they're going to be on the high end of anything you've encountered so far), so they'd definitely be useful contributions to your team right now, DK, but their skills are lackluster.
[top]Dragon Knights
The dragon knights are nice. Their stats are even higher than the pirate dragons and their active skills are WAY better. (Their leader skills suck just as bad as the pirate dragons.) They also have more useful typing -- what they lose by not having dual-element they make up by carrying subtypes in addition to Dragon, making it much easier to find a good team to use them on.
I've sorted this list based on my opinion of them (from best to worst) instead of the order they appear in the coin dungeon list.
The blue one, Cleopatra, is Dragon/Balanced, and she packs an 8xATK poison -- the strongest poison you're going to find on a non-REM monster. (AB Bluebird Blues has 10xATK but lower stats to back it up.) VERY useful.
The red one, Himiko, is Dragon/Healer, and has some of the best RCV you'll find on a dragon-type besides Angelion. She has Auto-Recover, which is nice.
The green one, Ishtar, is Dragon/Physical. She has a life-draining active skill, which is a useful thing to have on a physical team, and she has Two-Pronged Attack to boost her offensive power. Her main disadvantage is that she's not QUITE powerful enough to really stack up to some other choices.
The dark one, Mulan, is Dragon/Balanced as well. Probably the second-worst of the set. Her stats are slightly lower than the rest. Her main use is that she's got a reasonably good bind-heal active skill and a Resist Bind awoken skill (but just one of them, so she's not unbindable).
The light one, Jeanne d'Arc, is Dragon/Attacker. She's probably the least good of the set. She's got the best ATK and a Two-Pronged Attack awakening, so she hits hard, but her active skill is very limited in usefulness. Still, she has a place on the right team -- unfortunately, Attacker teams are hard to build.
All of the pirate dragons and dragon knights don't have to evolve, so you can farm up extra copies of them for awakening pretty easily.
The rest of the coin dungeons don't rotate out.
[top]Material Dungeons
Dragon Plant Infestation mostly exists as a convenient way to get lots of materials for evolving Pengdra.
The Alt dungeons are intended for endgame players who need to skill up monsters and have a lot of gold and stamina to burn, because the only useful things they drop are Flampy/Bubpy/Woodpy/Shynpy/Badpy and those are rare to show up -- you could drop a million coins and never even see one -- and the dungeons are moderately difficult.
Pengdra Village, King Carnival, and Together At Last are identical to the urgent dungeons that show up every few weeks. Most of the time it's not worth paying the gold for them, but Pengdra Village is the only place to farm Light and Dark Pengdra. If you're impatient and you need XP or evo materials, these dungeons are your friend. If you're patient, these dungeons are pointless.
Together At Last Rare Evo Rush is also ridiculously difficult. If you're patient enough to wait for the appropriate Daily dungeon, it's not worth running at all. If you're powerful enough to clear the dungeon (and keep in mind that you have to take down Trifruits and Keeper of Gold IN THE SAME DUNGEON -- those two fights usually recommend different teams) and you have millions of coins to spare, then you can run the dungeon if you're impatient.
And then there's Tamadra Village. It costs TEN MILLION COINS to get in and 99 stamina. For the first four floors you get a bunch of Baby Tamadra (50% awakening chance) with a rare chance of seeing a normal Tamadra. The last floor has you going up against a Tamadra, a red Odin Tamadra, and a green Odin Tamadra. That fight is trivially easy if you bring in poison; if you don't, it's annoying because you'll get bound a lot and the green one hits really hard, but it's not too difficult because they only have 30 HP. It's worth running, if you can.
[top]Rush Dungeons
Legendary Dragon Rush, Skydragon Rush, and Mechdragon Rush have to be the most stupidly pointless dungeons I can imagine. All fifteen of those dragons drop at very high drop rates from normal or technical dungeons. To make matters worse, the Skydragons *SUCK*. They don't even have good stats. The ONLY thing they're good for is skilling up the Legendary Dragons. And the Legendary Dragons aren't that good either; they used to be better than the Ripper Dragons (the elemental-resist dragons you get from the Pal Egg Machine) but the Ripper Dragons picked up ultimate evolutions with better stats and they're easier to level up. Their only redeeming point is that ONCE you get them fully leveled up they have some of the most powerful all-enemies direct damage active skills. (The mechdragons are a lot better. They're absurd stat sticks with pretty good active skills that can fuse Voltron-esque into a couple of gigantic god monsters with good leader skills and awakenings. When the Machine type gets introduced, they'll be even better. And Mechdragon Rush also occasionally spawns skill-up monsters for the Chinese gods and Metatron, so there is actually a reason to run this dungeon instead of the technicals, if you need these.)
The Ultimate ____ Rush dungeons used to be Special dungeons but now that they're coin dungeons they've been taken out of the Special rotation. They're all absurdly difficult, but they count as Descended dungeons (so the spirit jewels can show up), they all have a chance of spawning Extreme King Metal Dragon (a very rare evo material), and every monster in it has a chance of dropping and most of them are among the best non-REM monsters you can get.
EDIT: Yeek, that's a huge post. I should edit in some formatting to break up the wall of text.
EDIT 2: Formatting done.
EDIT 3: Sorted dragon knights in order of my opinion of usefulness.