Many times, companies have standard paperwork that they want you to sign and they don't want to deal with the hassle of hiring someone who won't sign the forms that their lawyers already drafted. Making modifications means that they have to call up their lawyer (who charges $300+/hour), have a conversation where the lawyer tries to convince them why they should keep the clause in, and then pay said lawyer to modify the contract. It's a hassle at the very least and it makes you look like a difficult person to deal with. So think carefully about negotiating on this, because it means less room to negotiate in other areas.
There are people out there who have a strong moral conviction against non-competes and who refuse to sign them. Power to those people. I don't care much for these agreements myself. But if you are thinking in practical rather than principled terms, I think it makes sense for many people to just sign the paper and move on.
What it comes down to is this: How likely are you to ever want to work for a direct competitor of this company?
If you are a chemical engineer working for a drug company, you are likely to find your next employment offer from another drug company and they very likely compete with your current employer. So be careful. But if you are a software engineer joining, for example, Dropbox, a non-compete might prohibit you from taking your next job at Box, Backblaze or any other online storage company, but it's very likely that you won't want your next job to be at a cloud storage company anyway, so think about that when deciding about whether to sign a non-compete.
In general, the more specialized your skillset is, the more you should care about non-competes. But as my lawyer once told me before I signed a pretty lengthy non-compete contract, "sometimes it's best to just sign the thing and not worry about it. You're almost certainly never going to work for a direct competitor anyway".
edit: Added emphasis above on the word "many", in response to rgbreneer's comment below. It's not that I don't think you should blindly sign non-compete agreements. It's that, like it or not, many employers don't like dealing with the hassle of someone who won't sign their standard paperwork. Maybe they don't care but their investors don't like it. Maybe it's a big company and the hiring manager doesn't want to deal with the bureaucracy of the legal department. Maybe they just really really don't want you working for a competitor. In any case, sometimes it's not worth fighting over. I once interned as a software engineer for a wristwatch manufacturer who made me sign a non-compete. The chances of me starting a wristwatch company or working for a direct competitor were close to zero. If that's the case for you, then weigh the risks involved, but you might decide that it's worth it to sign anyway.