Google now allows you to publish your blogs on custom domains automatically. And unlike the FTP publishing option, here you don't have to buy server space for hosting content. Google will still host the content for you.
Now the best part - even if you move from abc.blogspot.com to abc.com, your old links would still work and Google [via a simple DNS settting] will redirect the traffic to your new URLs. And the addresses of your blog posts saved on Digg, Del.icio.us would also work.
Just grab a web domain from GoDaddy or Google itself and instruct Google to start publishing content at the new URL which is minus blogspot.com.
This facility is currently available only for the new version of blogger. You can continue hosting pictures on Blogger Images or Picasa web albums. You can use this feature with domains (e.g. mysite.com) or subdomains (e.g. name.mysite.com). However, you cannot specify subdirectories (e.g. mysite.com/blog/).
Custom Domains on Blogger [Thanks rangaa, phydeaux3, Buzz]