Ever noticed something like [LION] or (LION) next to someone's name or in theire headline in LI? It stands for LinkedIn Open Networker, so that's a way to indicate you're open to all (or most) invites.
However: not everybody is fond of LION's, it could also scare off some of the people you'd like to connect with. There's somewhat of a debate between the "purists" (only link when you really know somebody) and "open networkers" (the bigger the network the better; some people even publicly boast how many connections they have).
So think carefully what method you choose. Also consider becoming member of SixDegrees group, this could massively increase your network in the shortest time (thanks again Dave!).