Signed an NDA but the company never returned their copy to me

For a one sided NDA, which is typical between a contractor and larger client, there's no need for two signatures. You sign to agree that you won't disclose anything and then you obey the terms.

For a two sided NDA, which may be more typical for an equal partnership, I would recommend against disclosing anything before they have signed the agreement and returned a legal copy to you. Feel free to look at any information they give you, but provide no input or feedback until they sign. They're taking all the risks by not completing the agreement, but you should still assume you are bound to not disclose anything you see.

In general, I try to make sure that any contract I sign doesn't result in an unlimited binding agreement before I sign it. NDA's should have an expiration date or condition. Something like a SOW (Statement of Work) should have an expiration date on the terms if not signed and returned. And even then, it's a good idea for the termination clause in the SOW to give you an out if something changes between when you first signed and when it was counter signed.

Just to clarify - for any contract to be enforceable, there must be consideration on both sides. An NDA that states that one party cannot disclose without putting some burden on the other party would not be enforceable.

In general, usually if there is no time frame for both parties to assent - then the time would be a reasonable amount of time. What is a reasonable amount of time? That depends ;) In reality, after 30 days (which has already passed) I would send a letter informing them of your intentions should they not assent and see what they say.

That said, just because you do not have a copy does not mean that they haven't signed.

NDAs are just a routine part of business at many companies. If they've been in business for very long, they probably have hundreds, if not thousands, of them with various counter-parties, especially if they're in a service industry. So, the most likely scenario is that getting your copy back to you just isn't that important to them -- the job of getting it counter-signed and returned to you is just sitting at the bottom of somebody's "to do" list.

As a result, if the NDA is important to you, you have to figure out how to bump it further up the to-do list. It sounds like you've tried the obvious: calling them and asking for it. If you're just fed up with them, you might try sending them a letter that says "Since we do not have a fully-executed agreement in place, I revoke my previous offer to be bound by the NDA. Please destroy the partially-signed version I sent to you."

Technically, a contract usually has to be executed by the signatories AND DELIVERED to be enforceable, but I wouldn't treat the NDA as unenforceable. I'd just follow its terms, whether you received the company's signature or not.

It depends on your role. It's normal if your is an employee/contractor. In this NDA puts restrictions on you only and signed by one party.