This question is one that I frequently get asked when training, especially from those people that are still quite new to LinkedIn and social networking.
My answer is always the same. You’ve got to accept connections that you are comfortable with, otherwise you’ll stop before you start.
I accept most connection requests that look like they come from real people, I’ll check profiles and activity if i’m unsure. Do they post regularly and contribute to conversation? I also look for a degree of relevance such as industry similarity or shared connections.
What I don’t do is accept connections that only benefit me. LinkedIn is a two way street and sometimes my knowledge can benefit others too.
If you don’t want strangers in your network don’t accept. Likewise if you have concerns about competitors then don’t. Just be aware that if someonw wants to find out who you do business with they don’t necessarily need LinkedIn for that. If you have NDAs in place with clients and receive connection requests that you are uncomfortable with then raise the question offline. Also remember security implications when you accept connections, some dodgy people may want to steal information from your profile.
Remember though that if you are using LinkedIn to generate new leads and business develop your network and audience is vital. A larger network potentially means more access to 2nd Degree connections, more chance of referral and higher visibility. Over time you’ll find a way of connecting that you are comfortable with. Whilst I believe depth of engagement is the most important aspect of social media activity a large audience is also beneficial.