Like all things, the law is different from state to state. So you first have to figure out which state has which law, because you might have an enforcible non-compete in one state that prohibits your taking a job, but be able to work for that same new employer in another state.
Most non-competes have some kind of choice of forum and venue clause in it saying what law is to be used to interpret the contract. In my state, the law was changed a few years back to invalidate any such clause - unless it was agreed to after the dust up arose. IOW, a company in Iowa could not force you in Louisiana to litigate the non-compete in Iowa, or using Iowa law favorable to the company...but that is not the law everywhere. They are not favored in my state, and the terms are strictly construed against finding it valid.
And in my state they cannot last more than 2 years. Even if it says for 10 years, it is only good for 2. And the contract has to identify with specificity the geographic area where it applies by city or Parish. In addition, if the employer goes out of business, or for only so long as the employer carries on a similar business in the area designated under the non-compete, then you are no longer bound. IOW, if you are a widget salesman who signed a valid non-compete, then if the employer goes out of the widget business, you are free from the effects of the non-compete contract.
In my state they can not only enjoin you from working, they can sue you for lost profit if you disregard the non-compete and its costs them money. Some states do not have recourse versus the employee for breaking it, they can just make you stop working. Others say you can be sued for money individually.
The thing is, it has to be a reasonable restriction. Not, "cannot work for any other employer so long as the sky is blue", which would be void. Some states require separate and "new" consideration (like Jake said). Some don't require any new money at all. Each state has some duration rule. They cannot stop you from working in your field forever. The geographic limit of the restriction varies state to state. Also, some states will let the courts modify the non-compete to something more reasonable and then enforce it, while in other states if it has a problem with part of it, it is all void.
I hate to say it, but you do not need to make a decision based upon what we do here - or some other state than where you live. But if you signed one, you might be able to get out of it by moving to a state that has favorable laws on your issue, whatever it is. See a lawyer.
