Here's my standard response (so much so, that I have a keyboard expansion for it - 'lkno'):
"Hi YOURNAME. Thanks for the connection request but I usually have a policy of only connecting with people I know, have worked with or otherwise have a pre-existing relationship. If we have met and I don't remember it please accept my apologies. If you have a particular reason for wanting to connect, such as a role or opportunity, I am happy to hear what that might be. Otherwise, please feel free to follow me on LinkedIn if you think my comments may be of interest. All the best. Regards."
I usually give them 4-5 days to respond. 9 times out of 10, they don't respond and I 'Ignore' the connection request. Of the remaining 10% that respond, there's probably a 50/50 split between 'No problem. I'll just follow you' (to which my response is 'Thanks for understanding') and 'Hey! Here's a great offer!' (to which I invariably respond with 'Thanks but I'm not interested at this time').
Very rarely, I will get an angry response from someone as if I've actively impaired their career. I don't bother responding to them. Even more rarely, the response is actually of interest and a conversation will ensue (and it may even result in a new connection).
That last extremely rare occurrence is the reason I don't just blanket ignore connection requests. Having been on Linked in since 2008, working as an individual contractor for most of the years since, and using variations on the above approach for most of that time, I've amassed over 1000 connections of which maybe 25% are recruiters.
There's no downside to adding LinkedIn contacts unless you're really into reading the curated feed or something. In fact, having more connections can be beneficial
