I have a blogger blog that is basically a list of new products our company offers. That is updated about 2 to 3 times a week I have about 10 different websites I would like this blog to be published on as part of the site what is the best way to do it?
Probably some form of RSS syndication. Note that Google will penalise you heavily for the duplicate content -- but if SEO isn't a concern, that doesn't matter.
It is best if you have one blog and you aggregate headlines to sites where you need them to be seen. Keeping one blog is best option for you because otherwise you have 9 more blogs to work out and make visible. My company has successful technology blog in our local market that brings us new customers (http://www.dt.ee/blog/). We show the latest headlines on our main page (http://www.dt.ee/). If somebody comes to main page then he/she can also go and read our blog to see if we are good enough and if somebody goes to our blog there is link in the header to get to our main page. You can do something like this: aggregate your blog headlines to all sites you need and have special panel in your blog sidebar where you list up sites your company has.