If you're like most people, you haven't really thought about this question.
But yes, there are times when you will be asked if you are Jewish, and you should answer a simple "Yes," even if you've had no conversion. (And even if you've taken no formal steps at all!)
Here are the usual suspects:
a) When you're requesting a religious accommodation. School, employers, meal requests, etc. They're required by law to at least try to accommodate you, and most (especially colleges) will do so easily and may even have standard procedures. My understanding is that they can't even inquire into your statements about your religion, except for clarification of the details or to request a letter from a clergy member. And of course, they can question if they think you're a liar :) That's normally cleared up with a clergy letter though.
My community rabbi was clever enough to come up with a letter for me to give to my school that satisfied my needs, but also didn't say, "I certify that this girl is a Jew." There is a legitimate worry there because people who are less-than-honorable can abuse these kinds of documents to try to "prove" a Jewish status that doesn't exist. Here's what the main part of it said (edited for privacy, of course): "Kochava attends and is affiliated with my congregation and practices orthodox Judaism. Because of this, she is strictly forbidden to work and take tests or classes on the Sabbath and Festivals." Then it went into an explanation of what holidays are included and an explanation that these dates don't correspond to the Gregorian calendar. That was just plain great writing for a conversion candidate.
b) When filling out hospital forms. Listing yourself as Jewish will send a rabbi to you instead of a preacher! G-d willing, you should never need the counsel of a chaplain at a hospital, but you want them to send the right one if the need arises! It can also affect the mortuary they call if you were to pass away in their facilities. You will probably be asked for this even if you're not being admitted. The hospital just wants this information in their records in case the day comes when you're brought in for an emergency. You might not be able to express your wishes if you're unconscious!
My take on this:
1) They have no right to inquire into your Jewish status and private life.
2) Most people who will be asking this question don't even know anything about Jewish status to begin with. Be thankful for the American Christian tradition that has trained people to think you are a member of a religion as soon as you say you are! (Even many American Jews believe this!)
3) If you did launch into the "No, but..." explanation, you've opened the door for them to try to deny you a religious accommodation.
4) If you've had a conversion already but are pursuing a different one, congratulations! You're definitely legally Jewish for secular legal purposes! You should have no qualms saying, "Yes, I'm Jewish" for these secular purposes.
BEWARE: Be cautious giving the simple "Yes, I'm Jewish" answer if you suspect that the person may rely on that information for the sake of a mitzvah. For example, if you are asking for a religious accommodation from a professor who is Jewish, there is the risk that the professor may one day try to count you in a minyan. However, you could wait to give the qualification until it actually becomes an issue. If there were a more direct connection between the statement and a mitzvah, tread carefully. Use your best judgment.
Can you think of any other situations when this rule of thumb might apply?