Based on how I choose fonts, and the fonts I've chosen for projects I've completed, I recommend:
1) Pick a serif you like that has enough variations (at a minimum, regular, bold, and italic, but I find a bold-italic useful from time to time) and use that for the body text. I always stay away from Times New Roman, because it's too darn common (so much so that I've come to loathe it). Some great examples already listed, to which I'd add Bembo, Adobe Jenson Pro, Janson Text, Poppl-Pontifex, Sabon, Perpetua, ITC Legacy Serif, and Warnock Pro. (There are some subtly different "looks" here... see item 6.)
2) Pick one sans or *very readable* display font that you like and use it for all the headings (except maybe the top heading level). Think about using small caps, italics, or differing weights and sizes to differentiate your outline levels. Strongly consider going no lighter in weight than boldface. You could also use the bold weight of your body text font for some of your headings (the bottom level of your outline, perhaps, or the top). Personally I try not to use Arial, Helvetica, Univers, or Zurich, because, again, they're too common (but I haven't yet come to loathe them). A couple good suggestions above, to which I'd add Optima, Myriad (Pro), Poppl-Laudatio, Du Bellay, Rotis Sans Serif, ITC Legacy Sans, Amerika Sans, Sava Pro, and Cronos Pro. (There are some very different "looks" here... see item 6.)
3) If you picked a sans in step 2, use this for captions and tables at its regular or light weight. If you didn't, pick one now for this purpose.
4) If you want, pick a "fancy" display font for one-off titles. Remember that the fancier a font you get, the less readable it is. This is where you can cap off your typographic choices with a neat bit of flair. I've successfully (I think) used Melcheburn, Amerika, MA Bastarda, King Arthur, Kelt Caps Freehand, Intimacy, Magna Veritas, Sherwood, ITC Rubino Sans, Cochin Bold, and Castiglione.
5) BE CONSISTENT. If you chose a black bar with a white bold, small caps sans as your Level 2 heading, stick with that throughout your document. If your body text is 9 points on 12 point leading, stick with that. And if you're using multiple columns, please make sure your text lines up across columns. It can help to make sure all your leading and "space before" values are multiples of the base value (if your body text is on 12-point leading, for example, make all your leading values multiples of 12).
6) BE CREATIVE. The "personality" of your work is partly dependent on the fonts you choose, so choose fonts that look good to you, that are readable, and that don't clash.
7) This one deserves its own item: Never, ever use Comic Sans. Ever. You don't need it. Stay away from it. Pretty much my nightmare document would be one that uses Comic Sans for most purposes, including body text, with Times New Roman added in for "flavor." Aargh!
HTH. HAND.
