Or maybe it’s more like “with what should I prime?” Both are good questions, and important to a painting project. The right primer, or lack of one, can make or break a paint job.
First, not all primers are primers, some “primers” are actually sealers. While many products do both jobs, it’s important to know which one you need done. A sealer will take a soft, or porous surface and solidify it and give the paint something to hold on to. This is the case on new drywall, the mud and paper are too porous for paint to stick to very well, a primer has to soak in and solidify the surface. It’s kind of like laying down tar on a gravel road in preparation for paving.
True priming does kind of the opposite; it takes a surface that is too smooth or hard for paint to grab on to and sticks very well so that a finish paint will stick to it. It forms a bond coat, like a layer of glue between the surface to be painted and the paint itself. This is the case on most new residential metal exterior doors. The factory whitish finish is often quite smooth and hard and most finish paints will have a hard time sticking to it.
Some surfaces, such as zinc coated steel, require special primers because of the chemical properties of the surface to be painted. Wood, especially cedar, sometimes contains tannins (which will bleed through the paint and show up brown) which require a stain blocking primer to hold out the tannins. A shellac based primer will work the best for this but an oil primer will take care of most tannins. Ordinary paint will never accomplish this task not matter how many coats are applied.
In many cases, especially with exteriors, choosing the right primer for a given surface is more important than choosing the right paint. A properly prepared and primed surface with an inexpensive paint will hold up better than an improperly prepared, unprimed surface with the best paint.
Having said all that, there are still some cases where a primer is not required. One fact to bear in mind is that paint will stick to itself. If this were not true, second coats would be impossible. So if you are painting over a paint that is similar to the one you are using, it is likely that the new paint will adhere directly to the old paint, provided there is nothing in the way such as dirt or wax, etc. This is most often the case in the case of an interior repaint, there is no need to re-prime the walls or trim since the wall or trim paint you are using will adhere just fine. One notable exception is in the case of walls or trim painted with old, hard oil paints, these usually require a primer as a bond coat. If in doubt, applying a primer will never hurt the final look of the project, it may just be unnecessary.
Another fact to bear in mind is that some finish products do not require a primer over some surfaces. Some latex paints, for instance, have very high adhesion and can be applied directly over fairly hard or shiny surfaces, such as oil paint. Some paints can be applied directly over metal, even if it is rusty. (Although it is also important to note that previously painted metal surfaces no longer count as metal from a paint perspective, you should apply the paint or primer that will adhere to the previous paint)