Blog Software are almost non-existent today as blog platforms provide online servers and domains to write and store. That being said, the giants of the blogging industry are Wordpress, Blogger and Tumblr. Wordpress has two variants (Wordpress.com and Wordpress.org). '.com' is free but has limited features but allows you to store your blogging. '.org' has better features and is considered the best blogging platform.
Blogger powered by Google makes monetising and analytics easier but is less flexible than wordpress and is good for hobby bloggers. It has a vast community and hence getting noticed is easier especially if you are a blogger. Tumblr is a microblogging site and is technically also a social network. Tumblr has less bloggers but is one of the best communities of the three. It's only drawback is that it is hard to monetize.