I got my current job--my first out of college--without any connections. It's a kernel programming job. I got it because I was able to talk intelligently about writing distributed systems and what a node-local kernel can do to facilitate distributed user-space applications.
That said, never underestimate the power of connections. I got my first internship because I "knew a guy who knew a guy". You never know when your scoutmaster or soccer coach or parents' friend from church or whatever unlikely acquaintance is going to end up working for (or founding!) the company that can provide you your dream job.
"...never underestimate the power of connections..."
Avoid overestimating the power of them as well; don't always assume it is who you know, or that who you know will make the experience better. When people err, in my experience, they seem to err in the direction of overestimating. They don't even bother to consider opportunities unless there is a connection involved, and they ignore red-flags they discover along the recruitment path simply because they have a connection there who downplays them. Often as not, they end up unhappy, but suffer through it because their only out is through more connections they don't yet have.
Sometimes, you have to look beyond the people you know.
That said, never underestimate the power of connections. I got my first internship because I "knew a guy who knew a guy". You never know when your scoutmaster or soccer coach or parents' friend from church or whatever unlikely acquaintance is going to end up working for (or founding!) the company that can provide you your dream job.