Yahoo is the most popular website in the world, probably because it was the first site that offered an Internet search feature. Not that Yahoo is a search engine, it is actually a directory, a very popular directory.
Being in Yahoo is very important, it not only helps with the traffic it brings in, which is substantial, but it will also help with your link popularity. Unfortunately Yahoo is often the hardest directory to get into, probably because it's the only major directory without a volunteer editor staff. You can submit sites to non-commercial categories for free, which is good for anyone who runs a content site, but submitting the free way is at best unreliable. The most efficient way to get in is to use the paid submission program, which will cost you $299 to get your website reviewed in 7 days. I should note that this only gets you a review, whether or not you are added is another story. At the start of 2002 they also made this fee a recurring yearly fee. So if you pay to get listed in Yahoo you'll need to pay yearly to keep that listing.
You can tell with your server logs if an editor is reviewing your listing. You should see a referrer with a URL of http://surf.yahoo.com/submissions/48975A/ or something similar. This at least lets you know when they've viewed your site, so you don't have to keep waiting for something that never comes. If they add your site, great, if not then submit again. If you can afford it I would suggest paying for inclusion, if only to speed things up.
Yahoo editing is highly irregular, a site that would not be added by one editor might be added by another. Also sometimes it seems they choose to just arbitrarily delete submissions. To increase your chances you should study the descriptions of the other sites in the category you are submitting to and try to mimic them as much as possible.
If you do choose to pay it doesn't mean you'll get added. Again in this area your fate is seemingly at the whim of an editor. Additionally they can add you but place you in the wrong category or with a bad description. They are supposed to send you a confirmation letter once your site is reviewed, if you want to appeal the editor's decision you are supposed to reply to this confirmation email. I had to write Yahoo support 5 times because they did not send me the confirmation email so I could not appeal the placement of my site. All in all the situation worked out and my site was placed in the appropriate category but it did not leave me with a very high opinion of the organization at Yahoo.
Despite all I've said Yahoo is in fact a necessary evil. You need to be in Yahoo, it's as simple as that. If you have to pay to get in then consider it an investment, if you're lucky enough to get in for free then congratulations.
Like the other two directories mentioned here recently Yahoo did away with their directory search results and now use Google for primary search results. Yahoo also recently bought Inktomi, so they may one day switch out Google for Inktomi (but they also own part of Google, so who knows). Yahoo's Google search results are peppered with some information from the Yahoo directory however, and searches at international Yahoo's do not always use Google. Yahoo also has a feature like ODP's "cool sites" which signifies good sites by placing them on top and putting a sunglasses icon next to their title. In the category listings Yahoo will first list sponsored listings, these are sites that are paying to be listed on top, your site must already be listed in the directory to take advantage of this feature, so its not a backdoor into Yahoo. After the sponsored listings Yahoo will sometimes list popular sites if it is a large category. Yahoo tracks every click made from its search results or from its categories to your site. Sites that get above average clicks can be placed in the popular listings, such sites may also get a ranking bonus in search results. If you have a good search results ranking it is very easy to get into the popular listings, it may take a month or so though because Yahoo only updates it's popular listings roughly once a month.