The dog's...

...bollocks, knackers, balls, etc.

1. When one thinks they are better than others (presumably because a dog can lick its own balls).
Usage: I can't stand that smug bastard... he thinks he's the dog's knackers.
2. When something is really good.
Usage: Nice motor, mate... it's the dog's.

I used this expression in front of the missus a while ago, and I've been really chuffed at how she has incorporated it into her everyday conversation.

I've been making a real effort to use as many similar expressions from the old country, not only to educate others but also so that they don't fall into disuse in my own conversation. Here are a few other animal related sayings:

As odd as cats' shite / dogs' balls

I've never owned a cat or a dog so I can't say for certain whether either of these statements are true. I can only assume that some eagle-eyed cat owner once noticed that their cat never seemed to leave any shit lying around, and that some perverted dog owner got his jollies by feeling his pet's clangers.

Usage: I wouldn't leave my kids with him... he's as odd as cats' shite.

As tight as a gnat's chuff / duck's ass

This one needs a bit more clarification when teaching the foreigner how to use it: (1) a gnat is a small fly (2) a chuff is another word for the vagina. You don't need to own a gnat to figure out that its gash must be pretty tight, well, compared to a woman's (bitchy gnats might sit around gossiping, "look at her, she's as loose as a regular sized fly"). The duck's ass reference is to with it being water tight. In both cases, they refer to people as miserable cunts, unwilling to spend money.

Usage: You haven't bought a fucking round all night... you're as tight as a gnat's chuff!

Hung like a donkey / stallion

You only really need to explain the word hung and the rest falls into place.

Usage: Would I be guilty of racial stereotyping if I said all black men are hung like donkeys?

I couldn't give a monkey's (fuck / toss)

Basically means that one couldn't give a fuck.

Usage: I'm leaving you, taking the kids, and shacking up with a lesbo.
           I couldn't give a monkey's.

It would freeze the balls off a brass monkey

I always thought that this was a nautical term (cannonballs - brass monkey) but I've just read about another connection to actual brass monkeys from China covering their testes. Testes... funny little word. Regardless of its origin, it just basically means to feel very cold.

Usage: Turn on another bar you tight fucker... it's cold enough in here to freeze the balls off a brass monkey.

Fucks like a rabbit

Again, I've never watched two rabbits fucking (think the reference is more related to the high reproduction rate than the actual speed of humping). There's got to be an animal lover out there who relaxes in a gentleman's fashion, feeling his dog's balls and watching his rabbits fucking.

Usage: It's said she fucks like the preverbial rabbit. You have a splendid opportunity of engaging in coitis.

The turtle's head

When the stool has already formed, gravity is now in charge, and there's precious little you can do about it... the faecel point of no return.

Usage: Fuck! Forgot me fucking keys... and me with the turtle's head.

The pup with the brown nose

Where the pup is an ample breast, and the nose is the nipple

Usage: Nice pups, luv... can I have the one with the brown nose?

Like a dog with two dicks

To describe someone who is very happy or content about a situation or outcome. This implies that a dog with two cocks would be capable of fucking twice as often, or possibly doubling the stimulation whilst cleaning its undercarriage.

Usage: What happened to him? He's walking about like a dog with two dicks.
           Oh, the missus finally agreed to let him put it up her shitter.

...hairs on its neck like a turkey

Not so much an expression as a line from a rowdy little ballad I learned as a lad:

Can you take it in your mouth Mrs Murphy?
Sure it only weighs a quarter of a pound.
It's got hairs on its neck like a turkey
And it squirts when you rub it up and down.

Not sure who Mrs Murphy was, but the line obviously refers to a cock.