Is it actually necessary for an average user to install any WordPress SEO Plugins?

Yes, all sites will benefit from some of the many WordPress SEO plugins available. How well your installation is already search engine optimised depends on your theme. Some themes are just designed for appearance whereas others are designed with SEO in mind.

Whatever your theme I would recommend installing two WordPress SEO Plugins as a minimum:

Site Map

Install a plugin to create and maintain a site map aimed at the search engines. "Google XML Sitemaps" is a good choice which, regardless of its name, will also support Bing and Yahoo. This plugin will enable the search engine spiders to discover all your pages and posts and will get them indexed as quickly as possible.

General SEO Plugin

Perhaps the most popular of these general WordPress SEO plugins is "All In One SEO Pack". You can simply install it with the default settings and all you have to do is enter the meta data for the Home Page (i.e. the text that will appear in the search results). The plugin also adds the ability to enter the meta data manually on each post/page. Whilst the default settings are ok, at some point it will be worth understanding what the plugin is doing (such as preventing the indexing of duplicate content) as some adjustments of the settings may be beneficial.

Another general plugin is the Platinum SEO Plugin. This is similar to All In One SEO Pack but has some more advanced features. Which one you pick depends on how deeply you intend to get into SEO.

Once you have installed these two plugins there is a wide range of others which you can install as well which address specific aspects of SEO. The following are just two examples:

SEO Slugs

One of the simplest WordPress SEO Plugins that you just install and leave to work. It contains a list of common words which it removes from a page/post title when generating the URL. This makes the URL search engine friendly as the keyword is more obvious.

SEO Smart Links

The aim with this plugin is the automatic generation of links both internal and external. You can define your own keywords and URLs for the link as well as controlling, amongst other things, how many links are created.

Whilst these WordPress SEO Plugins are very good it is important not to forget that content is the most important aspect of on page SEO. A site needs good, unique content which is added to on an ongoing basis. This content must also be optimised for the search engines, which means that you must structure your pages/posts around a keyword. There is a plugin to assist with this:

SEOPressor

Rather than helping setup the site for SEO purposes like most WordPress SEO plugins this one runs when a page/post is saved and analyses it for SEO purposes. The result is presented as a percentage (the higher the better) with recommendations.