Dmoz is currently the only search engine with all human editors. Given that fact, they have managed to index 3.5 million page with over 400,000 categories. Dmoz is unique because each site that is submitted must be reviewed by an actual human before it will appear in the listing. While it may seem “old-fashioned” to some, the result is a highly reliable index of only legitimate, properly categorized sites. Dmoz's directory structure is very hard, if not impossible to fool. In fact, although submitting sites are permitted to select certain categories, the human editors may place the site elsewhere if they believe it to be a better fit. This gives searchers the confidence that they will find what they are actually looking for when they enter a certain category.
The downsides? Well, it can take up to 6 months to get indexed, after submission. If you suggest an inappropriate category for your site, it can take even longer. The reason for this is that different categories have different editors. If one editor rejects the site and refers it to another, the waiting period starts all over again. While it may be a pain to get listed with Dmoz, it is well worth it. Many websites that will not ordinarily exchange links with a site that has a low (or no) PageRank will do so if the site is linked to by Dmoz.
Unlike most search engines, Dmoz listings are alphabetical. This means there is really no way to gain “extra” prominence over your competition. You will be placed in the appropriate category (whether you like it or not) and from there you will be listed alphabetically. If you try to beat the system here, by calling your website “AAAA ...” etc., the human editors will probably notice and refuse to list your site.