I've tested several options and found the Wayback Machine Downloader by Hartator the easiest to use.

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So, you have a website that's gone, for whatever reason, there's a copy in the Wayback Machine, and now you want to get it all back, preferably without clicking on every single page.

If you're lucky, the grab was done by Archive Team and the WARC file will be available in the Archive Team collection where you can just download the whole thing and then extract contents with one of the WARC tools like warctozip.

If it wasn't an Archive Team grab and the pages were just scooped up as part of normal Wayback Machine operation, things are a bit more difficult as archive.org does not allow you to download the WARC files for these crawls directly (and the data you want would be split across many grabs anyway as they tend to grab part of a site on one occasion, a different part later, etc.).

The Wayback Machine doesn't intentionally try to prevent you from downloading multiple pages, but the usual method of recursively downloading a directory with a tool like wget using the -np parameter does not work because the Wayback Machine date-codes URLs based on the time of crawl and so things which appear to be in the same directory are not. E.g.:

http://web.archive.org/web/20140208214426/http://archiveteam.org/index.php?title=Main_Page

links to

http://web.archive.org/web/20140215063724/http://archiveteam.org/index.php?title=Who_We_Are

which has a different date code, so as far as wget can tell they are in different directories and the crawl stops.

Tools to use
Wayback Machine Downloader by Hartator, small tool in Ruby to download any website from the Wayback Machine. Free and open-source.
WebsiteDownloader, website download service that let's you preview the results. Paid tool.
Wayback downloader, a service that will download your site from the Wayback Machine and even add a plugin for WordPress, 1 site is $15, 2 to 4, $12.50 and 5 or more is $7,50. Cheap way to get data back without setting up your own environment. Effectiveness unknown.
Wayback Machine Downloader Service Another service that recovers websites from archive.org. It has a free demo and offers unlimited downloads for $79. Not related to the aforementioned Ruby tool with the same name.
Waybackr, A new service that downloads, packs and sends to your email a copy of any website stored in the Wayback Machine. This service was free, but it seems to have stopped working.
Archivarix wayback machine online downloader, This service sends you email with zip archive of restored website. 200 files is free, first thousand files above this limit will cost $0.005 per file, every next thousand will cost $0.0005 per file....