The Festive Collection

There are five dragons in the Festive Collection:

Paradise Dragon    
Carnival Dragon
Tiny Dragon
Steampunk Dragon
Viking Dragon

Carnival Dragon is a Generation EX-II-b Exclusive Metal and Flame hybrid.
It's not breedable at the moment.
Hatching takes 20 hours.

Steampunk Dragon being a Generation II hybrid is the easiest of these to breed. It's pretty straight forward, flame and metal hybrid. Breeding and hatching take 16 hours.

It is easier to get the EX-II dragons by using hybrids as parents.

Paradise Dragon is a Generation EX-II Nature and Flame hybrid.
Breeding and hatching time are 20 hours.
Both parents need to be at level 10 or higher.

Tiny Dragon is a Generation EX-II-b Nature and Light hybrid.
Breeding takes 12 hours and hatching 16.
Both parents need to be at level 15 or higher.

Viking Dragonis a Generation EX-II-b Ice and Sea dragon.
The breeding and hatching both take 20 hours.
Both parents need to be at level 19 or higher.

The Gaia Collection

There are five dragons in this collection:
Seahorse Dragon    
Plankton Dragon
Aurora Dragon
Deep Forest Dragon
Hammer Dragon

Seahorse dragon
sea + nature
EX-II
Breeding takes 16 hours
hatching takes 20h

Plankton Dragon
Sea + Terra
EX-II
Breeding and hatching both take 20h

You need to have high level dragons to get EX-II-b dragons, preferably on level 20 or higher.There are reported instances when the parents have been on a lower level (like 19...)

Aurora Dragon
Electric + Flame
EX-II-b
Breeding and hatching both take 20 hours

Deep Forest Dragon
Nature + Terra
EX-II-b
Breeding and hatching both take 20 hours

Hammer Dragon
Sea + Metal
EX-II-b
Breeding takes 12 hours, hatching 16

The Legendary Collection

Legendary Dragon    
Wind Dragon
Mirror Dragon
Crystal Dragon

These are all legend dragons, which means they are Generation IV.

They are all breedable, the breeding and hatching takes 30 hours (2 days and 6 hours)

You need to have two pure/pure hybrids to get a legend dragon. It doesn't matter which other elements the parents have, they just need the pure element. I got my Wind with two Basilisks.

The Bizarre Collection

There are five dragons in this collection:
Gummy Dragon    
Soccer Dragon
Petroleum Dragon
Pearl Dragon
Jade Dragon

Two of them are Generation III - the Gummy Dragon and Soccer Dragon. 
Try Electric and Cactus (T+N) or Nature and Chameleon (T+E) to get the Gummy Dragon;
Dark Fire (D+F) and Fluorescent (E+I) or Medieval (F+M) and Alpine (T+I) for the Soccer Dragon.

Gummy Dragon
Nature and Electric
Breeding and Hatching 10 h

Soccer Dragon
Ice and Flame
Breeding and Hatching 12 h

Petroleum Dragon
Sea and Dark
Breeding and Hatching 16 h

Pearl Dragon
Ice and Metal
Breeding and Hatching 16 hours

Jade Dragon
Nature and Metal
Breeding and Hatching 16 hours

The Dragons in this collection have random elements.

The Frosty Collection

There are five dragons also in the Frosty Collection:
Ice Dragon   
Blizzard Dragon
Icecube Dragon
Alpine Dragon
Cool Fire Dragon

All Dragons except Blizzard Dragon have Ice elements.

Ice Dragon is Generation I dragon, which means that you buy the egg when you get to level 14. (Or get one as a present from your Dragon City friends).
Its breeding and hatching times are both 12 hours.

Blizzard Dragon is Sea and Flame dragon hybrid.
Breeding time 2 hours
Hatching time 2 hours

Icecube Dragon = Sea + Ice (Usually found in a mystery egg)
Breeding time 12 hours
Hatching time 12 hours

Alpine Dragon = Terra + Ice
Breeding time 16 hours
Hatching time 16 hours

Cool Fire Dragon is Generation III, meaning that it has two opposite elements; Flame and Ice. It cannot be bred directly from Ice and Flame dragons, you have to use hybrids, and good parents are
Alpine (T+I) and Medieval (F+M) or
Flame and Fluorescent (E+I) or
Ice and Hot Metal (E+F)

Breeding time 12 hours
Hatching time 12 hours

The Heavy Metal Collection

The Heavy Metal Collection consists of five dragons;
Metal Dragon
Gold Dragon
Mercury Dragon
Platinum Dragon
Armadillo Dragon

Metal dragon is Generation I dragon you get on level 18. (Or "get" - you can buy it when you reach level 18, with gold, but it's not too expensive.)
It's breeding and hatching time is 10 hours each.

Gold Dragon = Metal + Electric
Breeding time 12 hours
Hatching time 12 hours

Mercury Dragon = Metal + Sea
Breeding time 12 hours
Hatching time 12 hours

Platinum Dragon = Metal + Ice
Breeding time 12 hours
Hatching time 12 hours

Armadillo Dragon is a bit tricky, because it's Metal plus Terra, and these are opposite elements, which means that you need a hybrid to breed Armadillo. You need a metal hybrid with Terra or terra hybrid with Metal.
The easiest way to breed Armadillo is to breed Double Metal with Double Terra, but these dragons are exclusive and not breedable, so try with Metal and Flaming Rock (F+T) or Terra and Gold (M+E)
Like with the others, Armadillo Dragon's breeding and hatching time are both 12 hours.

The first 3 Dragons (when babies) have the same animation.
Metal, Gold and Platinum dragon look very much the same when grown up.

The Blue Planet Collection

There are five dragons in the Blue Planet Collection:   
Nenufar Dragon    
Waterfall Dragon
Coral Dragon
Penguin Dragon
Lantern Fish Dragon
All are Generation II, and the hardest part of collecting this is waiting to level 22 to get the Dark dragon and after that the Penguin Dragon.

Penguin and Lantern Fish Dragons are the only dragons that don't look like Dragons. Penguin Dragon is the only Dragon in the collection that has no Sea element.
(Double Ice Dragon plays with penguins and eats one of them...)

Nenufar Dragon = Sea + Nature
Breeding 6 hours
Hatching 6 hours

Waterfall Dragon = Sea + Terra
Breeding 4 hours
Hatching 4 hours

Coral Dragon = Sea + Nature
Breeding 12 hours
Hatching 12 hours

Penguin Dragon = Ice + Dark
Breeding 15 hours
Hatching 15 hours

Lantern Fish Dragon = Sea + Electric
Breeding 10 hours
Hatching 10 hours