But homemade mayo is a hard sell to some people, because they're worried about the raw eggs possibly getting them sick. Then there are people who are either allergic or sensitive to eggs, or vegans, who can't use an egg based mayonnaise, whether it's store bought or not. That's when vegan mayonnaise is good, because they're egg free, so free from the risk of salmonella, not to mention any of the health or ethical issues people have with eggs.
There are many egg free recipes out there for mayonnaise, but it seems like the vast majority of them are soy (tofu or soy milk) based, are dairy based, or just don't look right, don't have the mayonnaise texture, etc...
I played around with a recipe from the e-book, "The Everything Food Allergy Cookbook" by Linda Larsen, (which I downloaded free to my smartphone) and came up with this terrific vegan mayonnaise.
Its perfect! Same exact texture as mayonnaise, the only difference is that it's got a slightly more mustardy taste than regular mayonnaise. Works well in place of regular mayo in all recipes, whether its pasta or potato salad, in salad dressings, in egg salad, in tuna salad, you name it.