Normally, you can just select and copy text in PDF and paste it to a text file. Then save in UTF-8 encoding and put the file on the Kindle. It’s hard with big documents (aka books) though.
Another way is to save PDF as text (available in Acrobat Reader). The disadvantage is a complete loss of the document structure. The text is readable but not looking nice.
Recently I’ve found and tested on a 270+ page book this service: http://pdf4kindle.com/. It’s free and in my case has created a very nicely looking mobi file, which Kindle can read.