The equity has to come from somewhere.
If the company is public, and there is not an employee equity program already set up, it is unlikely that there is an easy way to give you equity through the company itself. If you really want equity, you could allocate part of your salary to purchase shares yourself.
If it is private, it also really depends on the company. More established ones without a culture of employees having stock options would be rather difficult to arrange this, I think. If there are investors owning a large percent, it is likely that the president of the company is trying to maintain > 50% stake, so there is a really limited amount of the company that would be fluid -- and other cofounders/ the first employees would likely already own those, and they would likely not wish to give up their own shares.
A newer company may be more receptive to the idea. They may not have the funds to pay a large salary so would be willing to be able to give up a few of their own shares in order to obtain a highly skilled employee for a minimum of 3 years (the term depends on the contract) at a smaller price in order to jumpstart the company.
If equity is something you are interested in, you really need to ask. I would not expect a large percent of anything unless you are a cofounder, though.