There is much debate about this. I can only offer my personal experience and also my take on the numerous articles that I've read.
RedWidgets.com is going to help you quite a bit in getting ranked in Google for the exact search term "red widgets"
RedBlueWidgets.com is not going to help you nearly as much for the search term "red widgets", although it will help you a little bit.
Naturally, you need to take care of the rest of the SEO as well, otherwise the domain name will not do you any good at all.
Some personal experiences on my own sites: vlcd.info which is ranked #13 out of 100,000+ for "vlcd" and nalmefene.info, ranked #13 for "nalmefene" out of 73,000. The point is these are new sites, just a couple months old, with very little backlinks.
Of course, these are not very competitive keywords, as someone said it's infinitely easier to get ranked for specific niche terms rather than the huge search terms.
One thing to remember is that redwidgets.com will help you immensely getting ranked for the search term "redwidgets" - that is, without the space. There seem to be quite a few people who type in their terms like that, without spaces. If you have a name with good PPC and nice search terms, you will get some traffic this way.
My personal experience: distancelearningmba.org (ranked #1 if you omit the spaces in your search), which gets the odd visitor now and then exactly like this, and gets high PPC so covers its own costs and funds a couple of other domain renewals, too. I have some others like this, too.
Good luck,
Josh