Below you will find several examples of a longish, real-world document, typeset using LaTeX, with the examples differing only in the choice of fonts for maths or text. In particular, you will find draft versions of two chapters of a book typeset in the following fonts for maths and text:
The LaTeX default; Lucida; Minion; Cambria; various versions of Times (MathTime Pro, XITS, and Tex-Gyre Termes); two versions of Palatino (Asana and TeX-Gyre Pagella), and Charter. There are also a few examples of mixed fonts, such as Charter for text and Lucida for maths, and Arno for text and Minion for maths. Each file is over 100 pages but only 1.5MB and can be easily downloaded. The LaTeX source file for each document is exactly the same except for a style file that sets the fonts used; that file is printed out in the preface to each document on page xvii.

There is virtually no hand-tuning in the document, and most hand-tuning will in any case fail as soon as the fonts are changed. The font sizes were adjusted slightly so that each example is about the same length. The book was designed and typeset by an end-user (i.e., me), and it has not been copy-edited.

For background on the book itself (first set in Lucida) see
http://www.vallisbook.org/
The examples below are from the second edition, which is in preparation.
Mathematical font design is an exercise in constrained creativity and is an under-appreciated craft. You may have favorites among the fonts - I do. Nonetheless, all of them required a considerable effort on behalf of the designers and some of them are beautiful.

If you have any comments send me an email (g.vallis at exeter.ac.uk). Or, if you think your comments may be of more general interest (typographic or TeX-wise), post them on TeX Stack exchange at this website

Latin Modern (the LaTeX defaults in xetex)

Latin Modern for main text, sans serif and mathematics.
PDF file

Lucida

Lucida for main text, sans serif and mathematics, all from Bigelow and Holmes via TUG.
PDF file

Minion

Minion Pro for main text, Minion-math (from Typoma.com) for mathematics, and Aller for sans serif.
PDF file

Cambria

Cambria (from Microsoft) for main text and mathematics, and Calibri for sans serif.
PDF file

Times fonts for text and maths

Times (Mathtime Pro from PCTeX) for text and mathematics, and Latin Modern Sans for sans serif.
PDF file

Charter (CHMath from Micropress) for both text and maths, and Lucida Sans for sans serif.
PDF file

Mixed fonts

Below are a few examples of using different fonts for text and mathematics. Mixtures can work well if appropriately chosen. The three things to try to match are: (i) The weight of the text and maths fonts; (ii) The aspect ratio of the fonts; (iii) The style of the fonts, which is a little nebulous. Thus, Charter has a similar aspect ratio to Lucida (both have a relatively large x-height) but is a little heavier, so the combination works quite well but is not perfect.