I use this when I want to setup a link or deep linking to my other sites.
You need a domain and hosting this can cost as little as $2 for a .info
Normally though I purchase an expiring domain that is in the same niche as the sites I want to link to. The older, more links, the better, but of course they cost money.
You setup the domain and hosting (hosting must have php/mysql)
Next step is to set up wordpress (now your saying wordpress isn't static)
You can leave the default theme or choose another theme you like.
Once you have wordpress setup you go to "Settings - Permalinks"
In the permalinks you place /%postname%.html (if you don't want .html change it to .php .htm or whatever you like)
Now changing the pages by hand is a bit harder but someone has written a small plugin which will change them to page.html and you could easily change the plugin to .htm or .php or whatever you needed. Plugin If you need help changing the plugin to any other extension let me know.
This allows you to setup a simple static html website, you can still use other plugins and widgets. If you have bought an expiring domain it is simple to get the original page names up and running without the need for writing 301 redirects. You can still add new pages as you want, though they will have the .html extension on them.
Total cost $0.00 (except for domain and hosting purchase)
Total time to setup about 5 minutes max.