"Take a photo" — why "take"?
Solution 1:
It seems to be an extension of taking notes.
From "The Language of Photography" http://www.source.ie/issues/issues2140/issue22/is22artlanpho.html
To photograph exists alongside to take a photograph, to take a picture, and so on. This is an extension of a broad meaning of take 'to obtain or set down', as in taking notes or statements, 'to set down or get in writing'; more directly, it is an extension of a use recorded from the 17th century onwards in structures such as taking pictures, likenesses, or portraits 'to obtain or get a picture'. The specific photographic use seems to have driven out uses in relation to pictorial art - nowadays, we paint, draw, or produce portraits, and make or do drawings - so that taking a picture can only refer to photography.
Solution 2:
In addition to the point made by Ronan, I think take belongs to the group of verbs that are semantically empty and are often christened delexical verbs. We often like to represent actions as nouns, often for maintaining an easy rhythm in speech.
So we 'take a walk', 'have/take a bath', 'have a read', 'have a look', 'take a dip', 'give a shove', 'give a laugh', 'make a promise' and so on.
In other words, don't think too much of the meaning of the verbs there!
Solution 3:
Photography is about capturing the state of some photons within a moment (well, a very brief period of time). Once captured, the information about that state can be taken with you and reproduced anywhere. "Taking a photo" amounts to collecting information from the environment and carrying it away, i.e. literally the act of taking.
Peter provides some good examples of how "take" can be used in other scenarios where such reasoning doesn't make sense (I certainly don't carry a tub around with me whenever I "take a bath") but I think in this case, a literal meaning can and should be inferred.
I think my answer might be similar to Ronan's, but not enough to be a comment on that answer.
Solution 4:
You can actually make photos as well, although to take a photo is more prevalent.
There are people on the Photography sub-site of StackExchange that determine their use based on what sort of action they are performing, noting subtle differences between to make and to take. See Does a photographer take pictures or make pictures?.