People have often asked me about how to get a better tone out of their flutes. Part of it comes from listening closely to yourself, as well as practicing with expressive phrasing (e.g. vibrato, tonguing techniques, etc.). A big,
big part of it is breath control, though. I've had a difficult time trying to find a good way to explain breath control when asked about it, but there are some basics that are easy to keep in mind. Some have already been mentioned here; for example, it is usually better to take in a new breath
before the old one runs out completely, like topping off your tank before it runs dry (though not
too soon before, or it can be sort of a waste). That will allow for more fluid note control as well as permit greater playing stamina in the long run. If you have to interrupt your phrasing too often to take in big, full breaths, then your melody may end up broken.
Something to consider is that the very end of a musical phrase is not always the best place to take in a breath. You may often prefer to sneak in a quick breath or two
during a phrase, in between notes, to let you finish a line or melody with a confident, adequate reserve of air at the end. You can experiment with your song to find the best place(s) to breathe, but if you wait too long before a breath, then the last few notes of a phrase might come up short and sound weak, or the first few notes of a new line might be overpowering. An important tip for taking in a lot of air quickly, which I learned back in my trumpet-playing days, is to always inhale
through your mouth! Don't be afraid to remove your lips from the flute for a split-second to take in air, because you'll be able to inhale a greater volume of air more quickly and efficiently than you could hope to through your nose. It might not seem like a big difference at first, but trust me...it adds up!

If you get the urge to exhale excess air while playing, then vent it out through the nose. It won't interrupt your playing to do so, because you can exhale through your mouth and nose simultaneously.
Something else that others have also mentioned already is the trick of filling your tank from the bottom up. For a really big breath, you should try to conciously start filling your lungs from the lower portion (the lower diaphragm, or "in the belly"), and then fill the lungspace above that, moving upwards as you go, all the way to the shoulders and neck if necessary. As you're doing this, try to imagine that your torso is like a glass being filled up with water, and follow the level of "liquid" (i.e. air) upward as it rises to the top. If you breathe just from the diaphragm, then you can't fill up all the way (which may be fine for shorter, simpler phrasing); however, for those
big breaths, you need to put some of your "accessory" muscles to use, such as in your abdomen, ribs, and shoulders. What you're doing there is optimizing the available lung space in your trunk to bring in a greater quantity of air, thus allowing for longer notes and/or phrases. With more practice, you learn to anticipate when you're going to need a fuller breath, and it becomes automatic and easier to do quickly.
There are a variety of exercises that you can do to practice breath control. Oitz listed a couple of good ones. I particularly like his first, in that it will allow you to get a better handle on maintaining both note consistency and an ear for self-critique. That's important for both tuning and expression. If you have a habit of letting your air flow drop off at the end of a note, it may turn out flat and just sound "off." On the other end of the spectrum, if you begin a note too forcefully, then you may get unpleasant squeaks, inadvertant overblows, and other such nuisance sounds. If, however, you use the same flow of air at the end of a note as you do at the start, then you'll have greater consistency and your tone will improve as a result. That may also help with your expression and phrasing, as your control of vibrato and dynamics becomes more consistent as well.
One breathing exercise that I sometimes recommend for wind instruments kind of builds on Oitz' idea. It's a consistency and stamina trainer. You can do it with or without a flute, though I prefer to do it with, because it gives you real air resistance and audible feedback to work with. You may also wish to use a metronome if you have one. To start, take in a deep breath, inhaling over a count of four steady beats (a tempo of around 70-80 bpm is usually pretty good for this). Make sure to fill up all the way on your inhalation! Then, exhale for a count of four beats using a steady flow, and try to expel the very last bit of air from your lungs on the
very last beat. Now, inhale for four beats again. Then, exhale for
eight beats, not expelling the last bit of air until the very last beat. Inhale again for four beats, and then exhale for
sixteen beats, keeping your flow steady until you empty your lungs on the last beat. The goal each time is to set your airflow at a constant rate to coincide with the time you have to empty your lungs, without altering it too much on the fly, and without running out of air too soon. You can do this ad nauseum, increasing the number of beats for your exhalation as you become better at keeping a steady flow of air (I usually finish the set at sixty-four beats for exhalation). This will help you to become consistent with your airflow, as well as to get a concious feeling for more precise control of your breathing muscles.
Hope this helps!