If a part is threaded, I use anti-seize... but it's just personal preference. Anti-sieze is generally used for threaded fasteners, although some mechanics use it for sliding pins in automotive disc brake calipers (due to high temps) and the like. Different formulas for different applications (copper, nickel, moly, etc.); I use Permatex 80078.

General purpose grease works for everything else.

One benefit of antiseize is that grit doesn't tend to stick to it as well as grease (which is more tacky) so you don't pick up dirt on the exposed parts. On the other hand, you are more likely to have anti-seize get all over the place when you are applying it. If you are handy, it's just good practice to have a bottle of anti-seize in your tool bag. If you are only going to do occasional work on bikes, it's really not worth the expense. Not that $10 is all that expensive in the grand scheme of things.