This is an interesting topic for blog owners and I have changed my own mind on this point over the years.
It used to be with most of our client blogs on Blogger, we set the blog to show 30 posts on the home page. Now with most of our clients using WordPress and many more home page options, we recommend having five blog posts on your home page.
I have seen some blogs where they just show one blog post on the home page or some that show three, but I personally like showing five blog posts.
If you have WordPress, you can even select to have a static page for the entry page of your blog and I have even seen some blogs where they simply show categories and snippets of posts like a magazine portal page. There are many flavors of what you should use for your home page.
Darren at ProBlogger did a review of this topic and I thought that the comments written in by other bloggers were very good. Here is the vote on the number in a nutshell.
Two Posts 1 Blogger
Three Posts 4 Bloggers
Four Posts 3 Bloggers
Five Posts 13 Bloggers
Six Posts 3 Bloggers
Seven Posts 1 Blogger
Ten Posts 6 Bloggers
More Than 10 Posts 2 Bloggers (1 had snippets the other had 35 posts)
So the consensus seems to match my thoughts five blog posts on the home page seems about right.