form_for prefers, as its first arg, an activerecord object; it allows to easily make a create or edit form (to use it in a "new" view you should create an empty instance in controller, like:
def new
@foo = Foo.new
end
It also passes a form variable to the block, so that you don't have to repeat the model name within the form itself. it's the preferred way to write a model related form.
form_tag just creates a form tag (and of course silently prepare an antiforgery hidden field, like form_for); it's best used for non-model forms (I actually only use it for simple search forms or the like).
Similarly, form_remote_for and form_remote_tag are suited for model related forms and not model related forms respectively but, instead of ending in a standard http method (GET, POST...), they call an ajax method.
All this and far more are available for you to enjoy in the FormHelperand PrototypeHelper reference pages.
EDIT 2012-07-13
Prototype has been removed from rails long ago, and remote forms have completely changed. Please refer to the first link, with reguard to the :remote option of both form_for and form_tag.