The Blogger free subdomain is like - abc.blogspot.com
You are quite able to earn money with this subdomain without a little money spending. But there are some hindrances of the subdomain. You know Blogger is a child of Google. So it's true that a simple push in your website is enough to get you indexed by Google but other search engines may delay in this. However, 95% of the whole search market is grabbed by Google. So you can remain tension free in this case.
Again, articles with the subdomain from Blogger generally takes a long time to be crawled and indexing by the search engines even Google. Sometimes its goes weeks, even months to crawl and indexing in search engine result page. But a custom domain may decrease this kind of problem.
You can use search engine webmaster tools to index your post. By inspect the URL option at google and submit URL option at Bing, you can do this.
One major problem having a subdomain is that you can't submit your website to the Adsense program manually or directly. You have to wait until eligible by Adsense in Blogger earning tab. But if you are having a custom domain, you are able to submit your website directly at Adsense.
Sometimes Blogspot subdomain may decrease your websites' popularity as it's free and long to type. As its free, many use it in their deceptive work.
However, your website having Blogspot subdomain doesn't damage organic visitors. So if you have a blog site and its visitors are only organic, you can use it. As Blogger is a Google child, it is ranked more easily and Google try to show a Blogspot site among the ten different results in the result page.