Backlinks are still important and are the main offsite SEO ranking factor, however the way Google values them has changed.
Now, it is much more about the quality, rather than the quantity of backlinks. Two or three backlinks from high quality, reputable and authoritative sites will help you to rank much more than dozens of ill considered, spammy links.
Additionally, the anchor text of the link matters, Google does not focus so much on keywords in anchor text now; in fact, over optimized, keyword laden anchor text can work against you.
The last thing to say is that Google looks at how backlinks have grown to your site over time and is looking for organic growth in your backlinks. If it sees to many artifical links in a short space of time, it may discount them.
Panda has changed the rules quite a bit!