When should I press garlic and when should I chop it?

That is actually quite controversial in its own way. If you are going to use a garlic press, you should cut the root end off the clove (you can do that a bulb at a time if desired) and give the individual cloves a bit of a crush with the side of a big knife before you press them. If you do that and you have a good garlic press, you can then just pluck the paper from the press to be ready for the next clove. That's fine, if pressed garlic is actually what you want.

Garlic is funny this way. It all depends upon how fussy you want to be. Pressing is about the least "perfect" way to prepare garlic for anything, but it pretty much works for everything. Many people find pressing to be the most convenient way to deal with garlic. If you press garlic you get fresh garlic juice and smudged garlic paste. For almost anything that is adequate.

If you desire for more than adequate, the kind of superlative awesomeness that Michelin Star judges look for and your little brother would never notice, then you need to break out the knife skills. Slicing, mincing, smearing, crushing, and even pressing give different results, even if those differences are barely apparent to us mere mortals.

I don't think ginger should ever be pressed, and I would not say that pressing is an always adequate technique like I would say for garlic. The best methods for ginger are to grate with a microplane or a ginger grater, to finely dice, to do it in volume with a food processor and then keep in the fridge or freeze in single use aliquots, or to roast and use in big chunks. You might find it helpful to know that you can freeze the whole hand of ginger. Frozen, you can use a microplane and the paper will just drift out of your way.

I'm not aware of anything else for which a press of the garlic press type could be of any use.

There are three factors to consider in deciding whether to chop or mince garlic versus using a garlic press:

1. Texture. If you want a sauce or dressing to be completely smooth, the texture of pressed garlic is suitable as it is essentially pureed.
2. Flavor. As a general rule of thumb, within limits, the more finely you chop garlic, the more strongly its flavor will permeate a dish. Crushing or using a press maximizes this.
3. Convenience. For a small number of cloves, a garlic press can be used without peeling the gloves. Of course, the press must then be cleaned, but some people find that easier than manually peeling.

In practice, professionals almost never use an actual garlic press because:

• They know the tricks to efficiently peel small or large quantities of garlic.
• For small quantities, with good knife skills, a press isn't necessary to get pureed garlic. It is fast and simple to get pureed garlic with nothing but a knife by smashing a clove or two with the flat of the blade, then mincing with salt, and smearing with the flat of the blade. This method does not require stopping occasionally to clean out the press.
• If larger quantities are required, a food processor will chop the garlic as finely as desired.
• Garlic in various forms can be purchased ready to use, from whole peeled cloves, to chopped, to pureed. Depending on the type of professional kitchen, and the results desired, one of these convenience products may be used to make things easier.

Garlic presses are convenient mostly for home cooks doing small quantities, who like the pureed quality of garlic it creates, or who hate peeling garlic. There is no circumstance in which they are essential.

As to other herbs suitable for a press, garlic is unique in its size and texture, making it uniquely suitable to a press.

I've done both, more mincing than pressing. Just from my experience, mincing is preferable for flavor, plus I watch MANY chefs on TV and rarely do I see them using a press, which speaks to me. Also, when you press, you have to go through all the steps unless you are willing to scrape the peel out of the press between cloves. If you press after peeling, you still will get residue you have to clean out between cloves. All in all, I think you get more flavor and less hassle by mincing.

There was an article on this on Serious Eats last year. The cutting method can give a different flavor depending on how much the cells are ruptured.

The takeaway was:

Knife-Minced: Once again mild, with little bits of chewable garlic that are tender and sweet.

Garlic Press: Stronger overall flavor than the knife minced, with a medium burn in the throat. It's a little sweet but also a little harsh.

Mortar and Pestle: Quite sweet with tender mashed chunks. Pretty tasty, with a very mild burn that sets in late in the back of the mouth.

Knife Pureed: The baby bear—neither too sweet nor too harsh, too mild nor too strong.

Microplane: The burn sets in faster than the others, with a slightly acrid taste, but not nearly as bad as raw. Unpleasant bitter aftertaste hangs in the mouth, but it's not severe.

However, in long cooking, the differences disappeared.

Pressed garlic is 4 times as strong as minced! So adjust your recipe accordingly if your going to use pressed garlic.