tl;dr: Wordpress (installing a Markdown plugin), Wikidot or, if you are a techie, Jekyll.
(My website is in Wikidot, I created for my group with Wordpress.
EDIT: Now I use Jekyll; here's why)
For personal homepages, lab notebooks and conference websites.
- WordPress - code and WordPress - hosting
- Simple wikis, very easy to create and manage
- Used as open science notebooks, for instance http://usefulchem.wikispaces.com/
- Showing small site by putting files into a Dropbox folder
- GitHub Pages
- Static websites with Git
- Wiki especially for mathematical collaboration
- Great for writing documentation
- Example (in Polish): http://django.carrots.pl/
- Jekyll-like static pages with built-in LaTe support, in Node.JS