What does it mean? 
It’s from here, believe it or not. It’s the latest craze on the Interwebs.
Translationally speaking, it means ‘Can I…?’
i.e. I can has cheezburger? = Can I have a cheeseburger?
Annoying, isn’t it? 
I asked a similar question.
It means, “I have the ability to do” something. For example, “I can tie my shoe,” or “I can get this project done by the end of the week,” or “I can post a response to a thread that answers the question asked, but not the one the OP intended.”
It’s half the title from a good song by The Pillows.
Internet Corporation for Assigned Names and Numbers.
wait… it no haz ekstra “N”
I can make a list of certain Dopers…
It means that I am skilled in the preservation of food using a certain method traditionally called “canning.”
ICANN has address on teh internets?
Every time we have a new thread on this, the question seems to get shorter and more vague. [del]Next time[/del] Tomorrow, when we have a thread on it, is it going to be wtf is ‘I’?
Holy crap! I just realized something! “I can…” at the start of the question is a very crude form of Black American English!
I say, ‘crude’, because it is not common, and is corrected when heard. But it is certainly not unheard of for small children to seriously ask, “I can have some more juice, Auntie?” or something like that. I just now made that connection.
Now, they would never, ever say, “I can has…”, but…
You know…now that I say it out loud:
“I can ha’ some more juice…” Oh my…that actually really is a sentence one might hear in AAVE. And as I say it out loud, I realize it sounds like “I can has”
It would be said with an entirely different inflection than the one I hear in my head when reading, “I can has cheezburger”, but still. That just blew my mind.
He’s a billionaire, so he can do anything he wants.
It’s new, from Apple!