Although most users do not pay for the services LinkedIn provides to them, the company has to make money some way. It does that by selling the contact and profile data to the users and companies that are paying for their LinkedIn accounts. That means that you will regularly receive messages from recruiters, analysts, advertisers, "partners", and other people trying to make a buck from you through LinkedIn.
Luckily, LinkedIn provides a page in your profile that allows you to block all these messages:
There you can adjust your settings to effectively block all this crap that is cluttering your inbox. We start with the Emails tab of the Email Preferences. There we click "Select the types of messages you’re willing to receive":
and we select Introductions only.
In the Set the frequency of emails window we set most of the alerts to weekly messages. This way, we limit the number of messages we receive, without loosing any information that might be important to us.
In the Select "who can send you invitations" window we keep the setting Anyone on LinkedIn. This way, people that found our profile are allowed to connect to us.
The Set the frequency of group digest emails window allows us to set the frequency of group messages to weekly.
We now move on to the LinkedIn Communications tab. There you find the settings for the sort of messages you are probably very willing to do without. We start in the Turn on/off LinkedIn announcements window, where we deselect "Yes, I’d like to get announcements, tips, and insights into new products and features.".
On to the next window, "Turn on/off invitations to participate in research", another one with would like to disable.
And here we are, already at our last window, Turn on/off partner InMail, where we deselect the "LinkedIn's marketing partners may send you informational and promotional messages." and "LinkedIn's hiring campaign partners may send you informational and promotional messages." options.
Now this should do the job and dramatically decrease the number of messages, especially messages without any value, that we receive from LinkedIn.