I had fun with this when I first got my own line a few years back…
“County Morgue, you stab 'em, we slab 'em, how may I help you?”
“Horses R Us…and what would you like to mount today?”
And a simple “sup” always throws people off I think.
Just in case you’re of the goofy nature that I am. 
“Eeeyello” is always annoying.
Oh! The “Greatest American Hero” song!
“Believe it or not, George isn’t at home,
Just leave a message at the beep.
I must be out, or I’d pick up the phone.
Where could I be?
Believe it or not, I’m not home!”
I always answer my cell phone with a confident Yes?. It let’s them know right away that I’m ready to get down to business, so it had better be important. It also sounds like I was expecting their call.
Depending on what kind of mood I am in it’s usually:
“Hi this is Liz”
or
“This is Liz”
Short and to the point…besides you have to pay for those cell phone minutes. You could do a full fledged opera on your home phone but on your cell phone (depending on your airtime) short and sweet is the best to go.
In rapidfire California twang voice:
“Fuckin’ Lars Ulrich - GO!”
Laughing… A LOT!
Joe’s taxidermy. You snuff em, we stuff em. How may I help you?
I often answer with a “Whattayawant?” since I was told “What?” was rude.
Sometimes I answer with “Milk?” as Lola often calls me whilst I am on my way home. I keep hoping for some hot phone sex but that might be dangerous while I am driving.
“Hello” also works in just about every circumstance.
“You’ve reached the late Edward Everett Historic Dairy Farm Legal Defense Fund Hotline–where there’s a will, there’s a whey.”
I’m fond of saying, “I told you not to call this number - what if my wife hears?”
On a related note, here’s the message I’m going to put on my cell phone’s outgoing voicemail message if I ever figure out how to do it:
“Hi, you’ve reached [cheffie]. I’m at home right now, but if you leave your name and number I’ll call you as soon as I go out.”
My voicemail message is simple “Hi, I’m not answering my phone, leave me your number…” blah blah.
“This is Richard” still sounds good.
Heh, as long as you don’t overuse it, it slays 'em every time. The last time I said it was in line at a fast food place in my small rural hometown. Someone behind me mumbled “Language!” and I was sooo tempted to start running around in little circles while ranting, “Dude! I’m fuckinLarsUlrich of fuckinMetallica, dude! I can say anything I want! Dude, I’m like so rich I bought the rights to every four letter word in six languages!” and then unleash a vehement barrage of foul-mouthed mayhem. But I didn’t. Drat.
And I have a friend who says “Ahoy hoy?” in place of “Huh?” and it’s really cute, for some reason.
Answer with the sound of a car crash. 
Local business names are always nice. Do you have any kind of a mental institution in the area? For example:
“Good afternoon, Willowcrest Instituton for the Criminally Insane. How may I direct your call?”
Or, like the Heavens to Betsy song “Terrorist,” you could open with: “I’m going to kill you! I’ll gut you and gouge out your eyes!” It’s an excellent icebreaker.
-Yd
How about like Cosmo Kramer…
“Go!”
Phouchg
Lovable Rogue