Let's see what happen depending on why you use LinkedIn.
- LinkedIn as a way to find business opportunities
In this case, you are more likely to be the one that sends invitation instead of being the one to receives them. You should accept a connection only if there is a potential business ahead, which is unlikely with cold invitations. Most of the time in this case you should ignore the invitation.
- LinkedIn as a way to find a job
Except if the invitation is issued by a recruiters or someone from a company you target, you should ignore the invitation.
- LinkedIn as a way to stay in touch with your network (via groups for instance)
Someone you don't know is not in your network, again you should ignore the invitation.
- LinkedIn as a way to show the world that your have a large network and that you're "important" in your field
If you are important, people already know you. If you want to be seen as an important professional, at least make sure that you have high quality connections. Ignore most invitation, apply a strong filtering.
- You are a recruiter - full time
You can accept anyone. The more people you know, the more chance you have to find a suitable candidate for your client.
As a conclusion: most of the time it seems better to ignore invitations. Even from people you know. Note that in many cases, people ask for connections only for the purpose of sending messages. Make sure that there is a public way to contact you and you will avoid most of the cold invitations.