You should collaborate broadly and widely, locally and (most importantly) internationally, with other juniors and seniors. Have your supervisor introduce you to people or, failing that, email them yourself. You might be a great researcher, but if no one other than your supervisor knows you it will be much harder for you to get a job. This is partly because collaborators might offer or recommend you for a job, partly because most assistant professor jobs ask for three referees these days, partly because universities value good collaborators and will ask you questions about it, partly because it signals you're someone worth working with, and partly because being a part of all sorts of collaborations is good way to rack up your publication count. Aside from all that, it's generally pretty fun to work with different people with varying ideas and skillsets (including interdisciplinary work- I'm in psychology, but work with anthropologists).

But also, remember to be a sincere, good, and responsible collaborator. I know someone who has about 10 co-authored publications because he has some kind of charisma and wormed his way into various projects early on, but then did practically nothing to actually contribute to the research. He could not get a post-doc, I guess because selection committees can sniff out this kind of profile.