Any and all discussions about Chinese buffets immediately turn into John Pinette quotes.
“You go now! You here four hour!”
When I’m at work, and customers thank me (I bartend) I find myself saying, “But of COURSE, DAHHHLING!” in the plummy tones of a rich old English lady.
I don’t know why I started doing it but I can’t seem to stop.
I also have an angry-old-English-man voice that only emerges when I’m joking around with one particular girlfriend of mine. And this voice says things like, “WELL, perhaps if you had CONSIDERED the repercussions of undertaking such a MAMMOTH ENDEAVOR when you were ILL PREPARED for the LIKELY CONSEQUENCES…”
I don’t talk like that. But the Angry Old English Man does.
Sometimes we laugh so much over it that we get a little teary-eyed. 
Since Ah-nold became governor, I pronounce all the syllables in Cah lee fohn ee ah.
Oh, I do this all the time, and I’ve offended people more than once, so I’m really trying to stop.
“So pretty!” is always with a Hindi accent - I don’t know if I picked it up from a movie, or a friend’s mom, or what.
“Antonio Banderas” is always “ahn-TOHN!-ee-oh bahn-DAY!-rrras!”
When I answer the phone with “Hello”, it’s usually with a Russian-ish accent (“Hhhieh-loh”), or sometimes sing-songy upper-crusty British (“Hel-LOOOO!”)
And a whole slew of phrases come out “country”, because you really can’t say them any other way: “don’t you pay it no nevermind”, “I’m fer it/I’m agin’ it”, “that was right neighborly”, “aren’t you a peach!” and so on.
I had an Iranian professor for a statistics class once upon a time. I often pronounce “basically” as “Basic-Alley” just like he did…
After spending a summer there, I can’t say “Fargo, North Dakota” without sounding like a parody of a native.
“Sorry,” when proffered as a perfunctory non-apology, is always pronounced in clipped British accent, flipping the R so it almost sounds like “soddy.”
If someone tells me an interesting story or fact, I never say, “Interesting!” I say, “Ve-r-r-r-r-ry in-ter-est-ing! But not funny,” in the Arte Johnson German accent.
Inconceivable. But it isn’t an accent so much as a voice.
“Oh really” in this weird clipped faux-British accent (I’ve heard it likened to the accent Leia puts on during her mouthing off to Vader early in Star Wars). My friends say I do this a lot and that it’s a really weird affectation, but I’ve never noticed it except on the phrase I mentioned.
Me, too. Thank-you, David Letterman, c. 1986.
I picked up a peculiarly American accented “Good evening” from the fella who voiced the “Rexall Family Druggist” on the commercial portions of the Phil Harris/Alice Faye show in the late forties and early fifties. Very serious. Very sober. Very clearly a piss-take, coming from me.
Likewise, “Bimp.”
Things you always say in a borrowed accent.
“Not fish… snake!”
“Quoite noice.”
“No Coke, Pepsi.”
“That’s thinkin’ with yer dipstick, Jimmeh!” 
I always scream, “I’m well aware of that Mr. Worf!” in Picard’s british accent.
Also:
“'allow? Whut’s thes, then?”
It’s not Picard, though. Just some random cockney thing I whip out.
“Cut me a switch of the tree, now! GEET!” In as deep fried, confederate Alabaman as you can.
Man, I’ve got a ton of these…
In my very best 'Strine:
Broooce
Shazza
Aw yea’?
(Bruce
Sharon
Oh Yeah?)
The “Shazza” comes from my vocal lessons, where my teacher is trying to teach me to rough up my voice, so in our very best Bogan we do “Shazza, yer late!” right through our noses untill I’m laughing to hard to do that anymore.
From my Kiwi friend at work, I’ve picked up
Aw shut brew
Aw cuz
Aye?
Chilly Bun
(Oh, shit, bro
Oh cous
Aye after every sentence, aye?
Chilly Bin - a cooler, called an Esky here.)
These are things I’m trying to stop doing, since I’ve noticed I’m somewhat of an accent chameleon, and I’m slowly losing my OWN accent.
Oddly enough, I can say “God willing and the creek don’t rise” without any accent whatsoever.
My only reliable slipping-into-accent is when someone says “Thank you” and I say “Thank yo [sic]!” in an accent that’s only recognizable as a Groucho imitation to someone who’s seen that movie. (Which movie? Is that Duck Soup?)