It depends on the context of where you are performing and who you are performing for.
"Hello, my name is Indigo Montoya, you killed my father, prepare to die" is a great line, but if you say it too often it gets a little unsettling. Walking up to someone wearing a trench coat and sandals and saying "Would you like to see something really special?" most likely will get you arrested. If you have television cameras and a crew following you, you can use David Blaine's monosylabalistic line, "Looook." I've found the best lines for family and friends, "I've just spent hours working on a new card trick, do you want to see it?", followed by "Please, it isn't as annoying as the one I showed you yesterday" after they immediately shout no and start walking away.
In reading that paragraph, you can get a pretty good sense of who I am as a performer. THAT is the goal of an introduction. So, start without the magic. Learn to say hello to people and start a conversation without a deck of cards in your hands. Talk to the folks at the checkout in the grocery store, the folks you see on an elevator, the people that are behind you in a line, the people you sit next to on the train, etc. If you can start a conversation with those folks, make them smile, make them laugh, make them react to you THEN you transition into magic.
A while ago, I was hanging out in a park in New York city with a bunch of other magicians. Two young ladies started to sit down on the bench next to where we were. I think I said something like, "be careful, you are sitting next to a bunch of magicians and if you sit there we are required to ask you if you want to see a card trick." They laughed and smiled and then we did card tricks until the started to slowly back away saying something like, "thanks for the warning, we have to go now...." I'm kidding about the slowly backing away part... it was more like running away. I'm kidding about kidding. They actually were really interested and enjoyed our performances.
One of my favorite jokes is "A magician asked me if I like card tricks. I said no. He then peformed five."
For me, a lot of people know that I do magic and they love my performances. I follow the John Bannon's rule. They have to ask at least twice before I show them something. Since they don't even ask once, I don't get to perform alot. But seriously, with family and friends, I just ask, "do you want to see something [insert adjective like fun, interesting, cool, strange]. If they say yes, I tell them, "unfortunately, all I have is a bunch of card tricks..." and they usually agree to endure several of them.