Yes it is relatively simple to import all of your posts from your blogspot or blogger.com site into WordPress.
WordPress has a built-in import function that automatically imports from all the following blogs:
Blogger Import posts, comments, and users from a Blogger blog
Blogware Import posts from Blogware
DotClear Import categories, users, posts, comments, and links from a DotClear blog
GreyMatter Import users, posts, and comments from a Greymatter blog
LiveJournal Import posts from a LiveJournal XML export file
Movable Type and TypePad Import posts and comments from a Movable Type or Typepad blog
RSS Import posts from an RSS feed
Textpattern Import categories, users, posts, comments, and links from a Textpattern blog
WordPress Import posts, comments, custom fields, pages, and categories from a WordPress export file
A Word of Caution if You have a Well Established Blogger Site
Moving the posts and comments and users from other blogging platforms to WordPress is not that difficult, but it does require some expertise, if your current site has some status in the search engines to setup the proper redirects on the old site, so that you can have any visitors that arrive via links to the old site get automatically redirected to your new blog.
Another potential issue is with images or pictures used in your posts. If they are embedded into your Blogger site, then they will need to be manually moved to the new site and each reference to the all the images in all of your posts will need to be edited to reference the new image location (on your new site). This can be a lot of work. If your site only uses images from Flickr, or you have uploaded all your images to a third party image hosing service, then you will not have any problems and all the images will still work once your site is moved to WordPress.
Here is an article that explains some of the issues to be considered, Blogspot to Hosted Domain Name : Feeds, Links, Search Traffic and Pagerank Issues.
WordPress.org also has a detailed page about Importing Content.
In the long run, a move to WordPress on a fully hosted domain will pay off with much greater freedom and possibility for your site. Not only can you take advantage of all the amazing free tools and services available for WordPress but since you have your own hosting and domain name you will be able to build out your site using other applications like plugins, forums, wikis and many others.
[Update – Jan 25, 2008] a new plugin has been released that performs a mapping and redirects all the old blogspot.com urls to your new WordPress blog. I haven’t tried it out yet, but a very promising new plugin for those who want to migrate from blogger to hosted WordPress.