It is possible to move and it is also possible to transfer all your current blog posts. Wordpress offers tons of great options for personalizing your blog. I actually offer this as a service "You can find out more info here http://awriterforhire.com/wordpress-installation/
I'm with Elaine on this one...I love WP, I had NO problems importing my old posts over from Blogger (although some of the spacing did get a bit messed up), BUUUUT...the fact that not all widgets and buttons work on my site is very frustrating.
I think if you pay for the WP site, that will no longer be an issue, but for now the free sites do no allow it. I have found that if I enter my own html coding and do a bit of extra work on my part I can make some things work, but overall it's the one flaw that I've found.
Good luck :)