Another one of those things that's ridiculously easy to make at home. Maybe it is or isn't cheaper than what you can find at the store. But you control what is in it. And you won't find it fresher or more delicious anywhere else.
1-2 tablespoon vinegar or lemon juice (adjust to your taste near the end)
1/4 teaspoon salt
dash cayenne or other red pepper
light grinding of black pepper
1 cup oil
In the pitcher of a blender, mixing bowl or food processor, mix together everything except 3/4 cup of the oil. Process for several seconds.
With the motor running, pour the oil in a thin stream through the opening of the lid (or into the mixer bowl). Continue until you've added all the oil. Go slowly enough that this takes about a minute.
Now you have mayonnaise.
Added paragraph 7/19/08: Taste and adjust salt, pepper, vinegar and lemon juice until the flavor balance is to your liking. You may like a more assertive mayo. You can get out your favorite commercial mayonnaise and do side-by-side testing until you have the seasoning tweaked just as you like it. Then write it down so you remake it just the way you like it ever after.
Put it in an old mayonnaise jar and refrigerate for up to a month. (Edited 7/19/08. I used to guess at two weeks, but I've since kept mayo for over a month just fine.)
A note on what just happened.
To "emulsify" means to mix together two liquids that don't like to be mixed together. Through the rapid beating and slow addition of the oil, the oil and egg have become emulsified. They're now beaten together into tiny little bubbles that reflect the light -- that's why the two transparent substances are now white and opaque.
A note on oil.
My understanding is that mayonnaise is classically made with extra-virgin olive oil. I don't like the heavy flavor when it's made this way; I'm used to clean, neutral tastes in mayonnaise. I use part olive oil and part neutral-tasting oil. I'm still searching for the most naturally made oil for this application. The one I made today was half olive and half corn. Peanut would also be a candidate.
Added paragraph 7/19/08: I tried a half peanut oil, half coconut oil mayonnaise. It's very coconutty. If you want a tropical effect from your mayonnaise, it works great. If you want a neutral spread, coconut is not the way to go..
A note on egg.
Harold McGee has a system for "safe" mayonnaise that involves using the microwave to sort of pasteurize the egg. You might be able to find it with an Internet search. It's also included in Mark Bittman's wonderful "How To Cook Everything," from which I got the basis of this mayonnaise recipe. But for myself, I'm not concerned about egg safety. We get all our eggs from free-range, healthy hens. Those horrible diseases occur in animals that are treatly horribly.
A note on acid.
Bittman says lemon is the perfect liquid for mayonnaise. I disagree. The mayonnaise I made following his recipe exactly (2 tablespoons lemon, 1 cup olive oil) tasted exactly like cod liver oil. It really was uncanny. I've been trying to use it up in tuna salad and fish cookery, because it turns everything milder into a strange fishy thing.