A HighRankings Forum member wants to know if it's possible to rank well for competitive keywords without having inbound links.
The answer is no. As Randy points out:
Without any links at all pointing towards your site not only will it not rank very well, but it won't even stay in the index.
Tis the way of the web. The search engines expect people to link to things those people find to be of value. So if no one ever links to your site they make the (correct) assumption that it has no value to their users.
If there's no trust (and no links to the site), there's no reason why the search engines would consider it valuable to other users.
The best scenario is to look for relevant sites, not only because Matt Cutts says so but because you can get great traffic from it:
I've noticed in my own experience that the best links are obvious. Highly relevant, quality websites. You hear it over and over, but my reasoning for calling them the "best links" is not merely for Search Engine ranking help. The reason they're so good is you can see that these referring sites send good traffic.
So in the end, links matter. Relevant links are better.
Forum discussion continues at HighRankings Forum.