Why it happens:
Your 2-year-old thinks that the world and everything in it (including her parents) exists for her benefit. Not only that, but her short-term memory isn't well developed, which means your child's impulse to say things right now before she forgets actually has a physiological basis. Therefore, the very concept of interrupting makes no sense to your toddler. She can't grasp that there are other people and activities that sometimes require your attention or capture your interest. This perspective also means that whatever directs your attention away from her (a phone call, for example) is by nature threatening.
Having your child obliviously break in every time you're chatting with a friend or scheduling an appointment is exasperating, but if you keep her worldview in mind, you'll realize that she's not purposefully trying to drive you insane. And don't worry, there is a light at the end of the tunnel. By the time your child is 3 or 4, she'll begin to understand what an interruption is and what the request "Please don't interrupt" means, and her short-term memory will develop enough that she'll be able to hold on to a thought (for a couple of minutes, anyway).
What to do:
At this age, your best strategies are to reduce the number of situations in which your child's likely to bust up your conversations, and to divert her attention whenever she does interrupt. Here's how:
Pick the right locale.
You can minimize your frustration by asking friends to meet you in a place where your child can play while the adults chat. A park with a sandbox is ideal — though your backyard might work fine.
If you and your partner are getting together with another couple with a child, the perfect solution is for two of the adults to watch the kids while the other two socialize for half an hour or so and then switch roles. Also, while it might sound like an extravagance, getting a babysitter to watch your toddler while you take a coffee break with a friend can do wonders for your sanity.
Read & teach:
A fun way to introduce the concept of polite behavior is to read your child such books as The Berenstain Bears Forget Their Manners, by Stan and Jan Berenstain, Babette Cole's The Bad Good Manners Book, Aliki's Manners, and the classic (and still charming) What Do You Say, Dear? by Sesyle Joslin, with delightful illustrations by Maurice Sendak.
Schedule phone calls:
Rather than battling it out every time the phone rings, the easiest solution is simply to make and return calls while your child is napping or after she's in bed for the night. Another tried-and-true solution: letting her watch TV or a favorite video, giving you a few uninterrupted moments. If you prefer not to use the TV, try redirecting your child's attention. You might want to keep a box or drawer of special toys or art supplies that get used only during phone calls. Or fill a sink with water and plastic cups for her to play with (as long as you can watch her), offer her a toy phone so she can talk with an imaginary pal, or invite her to participate by saying "hello." (Use this last suggestion judiciously if she's the gregarious type!) If your child tends to wander — or her attention does — putting a playpen stocked with interesting toys near the phone may be your best option. Getting a cordless phone can also help, as it'll let you move to a quieter room yet continue to watch her through an open doorway. On a sunny day you might try taking both the phone and your child into the backyard, where she'll find enough to do to grant you a few moments of peace. If your child isn't generally squirmy or if she's in a placid mood, holding and cuddling her while you talk might work; it will reassure her that she's important to you even when your attention is focused elsewhere.
Model the behavior.
Toddlers copy enthusiastically, so take advantage of this by setting a fine example for your child. If you and your partner tend to cut each other off, work on ending that habit. Also, try not to interrupt your child when she's talking to you. Any time you forget and break in on her (or anyone else), stop yourself and say, "Sorry. I interrupted you. Go on." With a little luck, your child will not only absorb your good manners but your ease in graciously admitting to a mistake. You'll also make your job easier down the road if she frequently hears you use "pardon me," "please," "thank you," "you're welcome," and "excuse me." While she can't yet put the principle behind these civilities into words, she'll sense it — because she'll find that it's pleasant to be around people who use them.
If at first you don't succeed, persevere:
At times you may feel discouraged — your toddler butts in for the fourth time while you're having a heart-to-heart with a good friend, or she waves a toy truck in your face while you're trying to wind up an important phone call. But don't give up; it's important for both you and your child that she learn the basic social graces, and it won't happen overnight. Participating in polite, respectful conversation is an important step toward becoming a social human being. What's more, if you don't curb her habit of interrupting, your powers of concentration will eventually become so fragmented that you'll no longer be able to finish a thought whether she interrupts or not.