Yes, it can be done. Here are 7 ways that a site can acheive increased link popularity without having to exchange links:
Directory Submissions - Submit to Open Directory and other sites like JoeAnt and Gimpsy. These are all human reviewed directories, therefore search engines will consider that your site must be of pretty good quality to be listed in them. Submission to these sites is free, but there can be quite a wait to get reviewed, since editors are unpaid volunteers. In addition to a link popularity boost, a listing in Open Directory will get your site listed in other Open Directory powered sites like Google's web Directory, AOL's web directory and many others.
Tips For Directory Submissions:
Editor Check - Is there an editor for your desired category? If not, consider applying. For Open Directory, this can give you power to add your site much more quickly.
Link Title - Don't try any tricks to get keywords in your title if they are not in your company name. This will get your listing edited if listing is approved or rejected outright. The title must be your official website or company name.
Description - Again, don't try to insert extra keywords here, it could backfire and your description will be edited or your listing rejected. The description should be short and concise. Just tell what your website offers and give some product or service examples if appropriate. Again, keep it short!
Be patient! - It may take weeks or months to be reviewed. If you've submitted before and are still not listed, try writing a polite note to editor of category to see if there was a problem.
Paid Submissions - Paid submissions to quality directories and portals is also a good idea. It is well known that a listing in Yahoo directory area will give you a good Google PageRank boost. Listing in Yahoo directory area is $299, so skip this option if your budget is limited.
Pay-Per-Click Search Engine Submissions - Google lists results of many smaller pay-per-click search engines. This can help link popularity if your site is listed in these results for your important keywords and phrases. There are hundreds of these smaller PPC engines that offer a free advertising credit just for signing up. Take a jaunt on over to PayPerClickSearchEngines.com for a good list of them. Submit listings under all your important keywords and phrases and include keywords in your title.
Affiliate Program - Having an affiliate program can boost your overall sales by letting other sites do advertising for you, but did you know that this can also help link popularity? For some affiliate program services like Commission Junction or LinkShare, they use a special link to track clicks and sales, so these may not be effective since they do not contain your actual domain name. The kind of affiliate program I am talking about is type that uses your domain name in tracking URL you give affiliates to use. Something like: http://www.yourcompanyname.com/aff?64340 As long as your affiliate program uses this type of link, then your site should see an increase in link popularity. Just make sure you offer a good incentive for affiliates so that they will add your link to their site. Even better, you can approve only related sites or sites with a good Google PageRank or Alexa traffic ranking into your program!