I was employed by someone for 21 months. Never were any taxes taken out of my checks. I recently resigned.. was handed my last check AND a 1099. I asked why.. his response.. I felt like it.. is this legal and might I have an unemployment claim?

Sounds like you were an independent contractor and not an employee. Did you also get a 1099 for 2103?

If you resigned, then you would have no claim for unemployment either way.

1099 is often used by some employers as a way to evade the employment taxes (income tax withholding, Social Security, FICA, unemployment compensation, worker's compensation, etc.). And OP may be forced to pay self-employment taxes if this "independent contractor" claim by the employer is legitimate.