I know! Right?!

It's pretty clear what the speaker is trying to convey: "I agree."

I agree with most of the other definitions, which provide details on the subtle context/audience-dependent connotations. I agree that phrase is annoying, used by speakers who use other annoying phrases like "my bad."

I would like to add to what has been said by providing side-by-side analogs; that is, alternative, equivalent but more acceptable expressions.

Example Expressions

I can't handle this idiot any more!
I know! Right?! OR Damn straight!

In wish I brought my swimsuit.
I know! Right?! OR You're telling me!

I like this 'double it for a buck' happy hour!
I know! Right?! OR You can say that again!

I was gunning for Miss Tipsy, but I just got shut down by her fat roommate!
I know! Right?! OR Join the club!

This is good sauce.
I know! Right?! OR Yes, it is.

Let's not go to the Bubble Club. It's so damn expensive!
I know! Right?! OR You got THAT right!

I have an idea: let's strip and go wallow in the mud puddles.
I know! Right?! OR You're preaching to the choir!

Our corporate holiday event was so cheap it was insulting.
I know! Right?! OR I couldn't agree more.

They are good at talking all sexy.
I know! Right?! OR Mmm hmm!!

This is the correct line for us.
I know! Right?! OR Right you are.

Tacos.
I know! Right?! OR Yeee-ah boooooooyeeee!!

We're in trouble NOW.
I know! Right?! OR No shit.

Tonight, we wear The Boots!
I know! Right?! OR Fuckin A right!