A machine shop I use regularly recently asked if I'd mind paying him by check to him personally rather than to his business, is this legit?

You can pay him any way he wants you to. If he doesn't report his income, you are not liable.

If this is your business expense (you pay for something to this shop and you intend to deduct this expense on your own taxes) then it does make a difference and you should refuse this request and continue paying to the business. And even if it makes no difference to your own taxes, if you have a reason to believe that the shop owner wants to avoid taxation, you should also refuse to "accommodate" such a request. There is no legitimate reason why a shop's owner would make such a request other than an attempt (a futile one, mind you, if that business is audited) to evade taxes (and tax evasion is illegal, as we all know).

So long as it is less than $600 OR this is not a business expense you plan to deduct, you're fine. Otherwise, you need to plan to issue a Form 1099 and will need to know how to complete it.