Google, Yahoo & MSN account for more than 95% of all searches in the world. Yes you might get a couple of visitors from other search engines but your results will be minimal compared to what the big 3. It's important to know how each one of these will vary as far as how each search engine will rank you their search results.
MSN is widely considered the most undeveloped search engine out of the big three. MSN also has the lowest share market out of the three. This occurs mostly because the spider bot crawls only the beginning of the pages (as opposed to the other two which crawl the entire content) and also the number of pages found in its index is extremely low. This means MSN is much easier as far a SEO is concerned. This makes MSN the most susceptible search engine to the use of traditional SEO techniques. Meta tags, keywords in the title and the introduction play a major part in the keyword analysis. I would note that strong link building is a must. Another downside of this search engine is its habit of supplying the results based on geo-targeting, which makes it extremely hard to determine if the results you see are the same ones everybody sees.
Yahoo follows the same set of factors as Google. There are several Differences; the most important one being is that Yahoo is the most accurate search engine when it comes to counting backlinks. It is not unusual to see a ratio of 20 to 1 between the number of backlinks calculated by Yahoo and those calculated by Google. Lately it seems that Yahoo has incorporated the LSI factor too, which makes it less vulnerable to keyword stuffing techniques.
It also seems that Yahoo has begun downgrading the importance of the links built entirely for SEO purposes (like the ones from directories) and gives more importance to natural backlinks. There have been reports that many websites which have performed well in the past few years have begun losing SERPs because they concentrated on artificial linking. Another reason thought to be the cause of this downgrading is the irrelevance of the anchor text used, in relation with the content of the website containing the link. Yahoo is increasingly becoming a favorite among SEO marketers, because it helps them (especially through the site-explorer feature) to better understand how well their website is doing in terms of backlinks and can also be used to predict fairly accurately if your SEO effort is working well. Another major difference is that the crawl rate of the Yahoo's spiders a at least 3 times faster than Googles. Another thing to note is that Yahoo still reads the keywords meta tag. and still gives credit to for a relivent description meta tag.
Google is the most well known and most used out of all three and greatly benefits from the undivided attention of most SEO marketers. The SERP for a keyword in this search engine is based on a huge variety of factors (some count approximately 200 and this year reported 450 new changes). However the most important ones are: the number of backlinks and the authority of the backlinks which together help in calculating the Page Rank, the anchor text, the relevance of the page containing the link to the anchor text used, the content of the URL, titles, and the relevance of both the page that sends the link and the one which is being promoted relative to the specific keywords optimized.
As a side note it is important to know that the PageRank value used in the SERP calculation is not the one you see in the various online tools or toolbars, the PR that you see there is the outdated version established at the last wide Google update. The relevancy of a text is not determined solely on the keyword density of the primary keyword aimed, but also on the basis of latent semantic indexing or analysis.
LSI is used to determine some additional keywords based on the analysis made on a large number of sites and which helps deciding subsequently if the aimed keyword is present there naturally or for artificial SEO purposes (based on the presence of these additional keywords). Other peculiarities associated with the Google search engine is the low number of backlinks it determines as genuine (mostly because Google divides webpages in to separate indexes: main and supplemental) and the enforcing of the nofollow tag. And of course there is the sandbox, the limitation of new sites to rank highly for very competitive keywords. This in effect means that Google places great value on the age of a domain.
The top position which Google now enjoys is also determined by the ability of the spider bot to crawl nonstandard formats like . PDF, .DOC and .SWF (flash files). This in turn is changing because Google has now anounced that they can infact read .swf & .pdf files. Another factor which seems to heavily influence the SERP, especially for low to moderately competitive keywords is the freshness of the content. This has resulted in the phenomenon called "Google bump" which tends to bring new websites traffic, despite the low number of backlinks and the absence of any perceived authority. Quite often, this turns to be more than a lucky fluke especially when the website in question is updated on a regular, frequent basis.
In conclusion it is quite obvious that Google, the most important search engine, is the hardest to penetrate and achieve high positions for competitive keywords, while MSN which holds the lowest market share is the easiest to dominate. Yahoo has recently changed its policy and is now harder to manipulate and to its merit also holds the most accurate backlink count. It is possible to build an SEO strategy aimed to play the peculiarities of each search engine, but in the end it is recommendable that you aim to obtain high SERPs in all three of them and gradually adapt your strategy to avoid any possible penalty in the long run. If you focus your SEO stratagy on solid tecniques you can rank #1 on all three search engines.