If you read LinkedIn's own connection advice, you will see that it is supposed to be about connecting to people that you actually know professionally. This is oftentimes not the case, however, as more and more people are connecting to strangers for various reasons.
LinkedIn Open Networkers (LIONs) seem to view LinkedIn as a big competition, to see who can connect with the most people. Others just like to expand their networks because they realize that it's to their advantage to allow many people access to their profile, which may lead to an opportunity when someone with their skills is needed. Still others may read a post or comment within a group or the Answers section and decide they would like to connect for some perceived value.
Whatever the reason, sending a blind connection request to someone who has never heard of you requires a bit of finesse if you want a positive response. If you're in the habit of clicking on the "Friend" relationship designation and sending the stock LinkedIn message, you just might find yourself out of luck and reported. Multiple reports from users who don't know you may actually get you banned from LinkedIn, so don't do it!
A better tactic is to draft a brief message explaining why you would like to connect with the user and how that might benefit them. Here's an example:
"Joe, I read your recent comment about video production, and I would like to connect with you. I have clients who need such a service from time to time, and we may be able to work together."
When Joe reads that message, it is likely that he would perceive value in connecting with you. Worst case scenario, he can click ignore, but it is unlikely that he will report someone who took the time to draft a nice, personal message. Courtesy goes a long way in social media, just as in person.