In other words, you received unwanted invitations to join people's networks. (I don't like the use of the term "spam" in this context because it is ambiguous; people use it to mean very different things.)

I think I know how some of the unwanted invitations come about. I've been guilty of accidentally sending out a few of these myself. When you join LinkedIn, you can have it search your e-mail address book for people who are already registered on LinkedIn (actually you can do this any time, not just when joining, but it is one of the things that is offered when joining).

Most people's e-mail address books contain hundreds if not thousands of contacts, and the list of "matches" (e-mail contacts who are already LinkedIn members) can be quite long. Therefore, before sending out a bulk invitation to all the matches, you have to go through the list and cull out the ones whom you don't really know -- i.e., people you've corresponded with once or twice by e-mail but don't know personally, etc. If you're too sloppy about this culling process, you'll end up sending some unwanted invitations.

There are of course other ways you could send or receive unwanted invitations. For example, you might be in someone's 2nd or 3rd-order list of connections and they decide they want to connect to you directly.