In short – no, meta keywords should not be used.
Back in 2009, Google’s Matt Cutts discussed the engine not using the keywords meta tag to determine SERP ranking:
Google officially ignores the keywords meta tag, thanks to the black hat SEO tactic known as “keyword stuffing”. Many so-called webmasters used to stuff this tag with high-traffic keywords to garner more site visitation, regardless of relevancy. By the late 1990’s/early 2000’s, the tag was predominantly unsupported, and is now regularly frowned upon by most white hat SEOs.
For more related to other search engines, read about Bing’s and Yahoo’s standpoint on the meta keyword tag being used as a ranking factor.
If you want to know more about the different parts of meta tags, check out my post on meta descriptions.