I recommend Behance.net. Free, unlimited everything, and it's a massive and very well-respected platform for creative professionals to network etc. Even has job listings. Best place to put your portfolio online in my opinion. I've gotten lots of work just from being part of Behance.
They also offer the new ProSite service if you want a fully customizable site with your own branding etc, which ties directly in to your Behance portfolio. Gotta be on Behance these days.
Check out Bandcamp. They even offer a way to sell your stuff if you want.
Or Newgrounds Audio, which has a layout that not everyone might like, but they seem more geared towards music/sound for games, whereas Bandcamp is mostly about music from the artist's perspective.
Or dive into Wordpress and integrate Soundcloud and/or Audioboo with it. Lots of options and flexibility there, but also a steeper learning curve. You can host a Wordpress blog on wordpress.com for free, or get your own hosting solution and install it there for even greater freedom (and more effort).
I'd definitely vote for Vimeo/Soundcloud. Buy the soundcloud basic membership, which gets you more than enough space for an average portfolio of a few years, plus you can organize your material into "Sets" (e.g., film sound design, game sound effects, music production, etc.). I would recommend using one of the many free website designers out there to organize your sounds into a site with descriptions for each example, then embed your vimeo videos and soundcloud sounds in that site. Keeps things neater.
GoDaddy hosting and Wordpress with a premium theme is my choice, then nicely embedding Vimeo and Soundcloud content in. Wordpress even has plugins and shortcodes specifically for Soundcloud etc though I personally use the nice 'Artwork Player' embed code from Soundcloud itself.