I have found myself doing this in a couple of situations where I was really interested in the work. I don't mind it so much as long as the client pays for the spec work, but they usually don't want to. As a rule, though, it's best avoided.
Judging from your site, a client can look at your work and tell what he or she is going to get. That should be enough. It usually means the client is inexperienced in dealing with illustrators and unfortunately there are too many of us who are inexperienced in dealing with clients. Freelancing is the major facet of illustration nowadays, and the schools do not spend nearly enough time, if any, on this fact.
Some things that will change your professional life are:
Don't do work on spec.
Target sample mailings to clients who use the type of work you do.
Never do Work for Hire.
Limit revisions to one or two. Charge for more.
Give the client a Letter of Agreement immediately after the first time you speak. (A boilerplate can be found here
, and there's a link to download it in PDF format.)
As it usually turns out, the less a client is paying, the more they want to micro-manage and art direct and want something for nothing. The higher paying clients want you for the style they see in your portofolio and are often much easier to please.
Once upon a time, an illustrator could buy a new car and put a down payment on a new home with one good gig. Those days are obviously over, but the situation only gets worse the more we undervalue our own work. The hardest thing any one of us can do is say No. The first time one does, it ultimately is an uplifting experience (if you don't count not being able to pay the utility bill occasionally). The highest-paying job I've ever been approached with, I had to say No. But it's made life easier.