There's a lot that's been written on the subject of impedance matching, and much of it is available to read online, so there's really no point in giving a lengthy explanation here. For the average audio engineer, it reduces to a few fairly simple rules that will keep you out of trouble most of the time.
For maximum signal voltage, load impedances should be much higher (ten times or more) than source impedances. This is the condition you're concerned about at least 90% of the time when moving audio around your studio. For instance, if your microphone has a source impedance of 150 ohms, your mic preamp should have an input impedance of 1.5K or greater.
For maximum power transfer, load impedance should equal source impedance. We're generally not concerned about power transfer except when driving transducers such as speakers, cutterheads, and so on. And even then, it's typical that the power amp is designed to have an output impedance lower than the load impedance anyway, for better damping.
An audio transformer should have ONE of its windings (primary or secondary) terminated in its rated impedance for flattest response. For instance, consider a 1:10 mic input transformer, which could also be called a 150:15K transformer. (The impedance ratio is the square of the turns ratio). For best response, either the primary must be terminated with 150 ohms, or the secondary with 15K. The source impedance of the mic itself provides the 150 ohm termination for the primary, so the secondary should be left unterminated, or bridged by an impedance much higher than 15K.
Passive filters tend to be fairly critical as regards source and load impedances since these impedances usually form part of the filter itself in actual operation.
These last two items are why some older gear seems to violate the first rule I gave; in other words, this is why you need to terminate the output of your old transformer-coupled tube line amp with 600 ohms even though it reduces the output compared to running it into, say, 10K.
Here's some good reading for you:
http://www.richardhess.com/be/aes-80.htm
http://www.svconline.com/mag/avinstall_transmission_lines_why/
(Note that in the second article, whoever typed it up subsituted "V" for the ohms symbol for some unknown reason).