|Your own blog(s)|
Wordpress, Blogger, (both?)
I have a wordpress blog, does it make sense for me to also have a Blogger account and post entries there? StumbleUpon? Typepad? I would be doing this solely to get any traffic that my word press blog which I host may have missed. Does anyone do this? Is this a stupid idea?
If I were you, I'd stick to 1 blog. That way, you don't have to worry about maintaining/promoting 2 blogs. Make sure your Wordpress blog is perfect - on-site SEO, layout, the works. Then, promote the heck out of it.
Ditto. First, Google does not like duplicated content. They penalize sites for that. Secondly, Google is pretty clever and can detect "tricks" like you're talking about.
Hubie -- I have multiple blogs and websites (in my personal life, 100s in my professional life), but each have a clearly defined subject, voice, purpose and type of content. When relevant, I occasionally link between them, but that's pretty rare.
The idea that you use different platforms for the same content doesn't make sense, as others have correctly said -- an analogy would be an author publishing the same book with different publishers.
A good way of thinking about this is that Google pretty much knows about all websites regardless of how hard you try to prevent it from doing wo -- it's effectively omniscient. You can help Google by telling it about your site (Google Webmaster Tools rock). People don't find things by seeking out Blogger sites or TypePad sites -- they go to Google (or StumbleUpon, or Del.icio.us, or ... well, mostly Google).
Please your readers by creating a great site. Let the world know -- Tweet about it, list it in all your profiles, put it on your facebook page, and listen to what people have to say.