What kinds of checks are we talking about? Businesses do all kinds of payment by check, and there are relatively few times that tax withholdings are required. The major one, of course, is paychecks, which I presume is what you’re talking about here, but you need to be more specific.
Are you a direct-hire employee of the company? Or are you a contract-hire of some sort or independent contractor? If you’re classed as an independent contractor, then you’ll have to file an income tax statement showing your “corporate” earnings (if you’re set up as some kind of corporation), and include your income and self-employment taxes as well (including the personal and employer portions of FICA and Medicare tax, up to the earnings caps).
And yes, if you’re receiving this payment as any kind of employment-related earnings, then the company making the payments will send you (one presumes, based on the fact of you not being a direct-hire employee) a 1099 form so that they can deduct the payments made to you as a business expense. So there will be a 1099 form with your name on it, and IRS will be expecting an accounting of those earnings – and the tax due on them.