I don't know about system-wide fonts, including Apple's traditionally tiny font for its own menus, but at least for Apple Mail there is a partial fix:
(1) In Mail, click on "Mail" in the upper left corner of the screen (right next to the image of an apple).
(2) From the drop-down menu which appears, click on "Preferences"; it's second from the top.
(3) A little Preferences box will appear. Click on "Fonts & Colors" (in the middle of the top line).
(4a) In the Fonts & Colors box, there are three lines: "Message list font", which apparently isn't adjustable; "Message font" and "Fixed-width font", which are adjustable. (I'm not sure of the difference between the three - I normally use Gmail - but "Message font" is the one which affects the size of the message text, though not the header.)
(4b) Next to "Message font" is the style and size currently set, and at the right, a button which says "Select...". Click on Select.
(5) A new, separate box appears with four columns. The first three allow you to change the type style.
The fourth column (far right) is your font size. Click on the size you want, or use the slider to choose a size in between the numbers they offer.
(6) Close the boxes, and mail away!
(7) Caveat: This only seems to affect messages I am composing in Mail. I have my Apple Mail account tied to my Gmail account, and when I view my inbox in Apple Mail, changing the "Message font" does not change the font size the same way; but hitting the [command] key and the + or - key (at the same time) will do so. Again, I don't know whether this is the way Mail normally works, or just the way it works when it's tied to another mail system.