There are a very large number of sites out there offering to host your blog for free. There are as an example many thousands different sites that provide free word press hosting on their wordpress network sites (earlier wordpress MU). WordPress is however only one of many different free blogging platforms and I will there take a look at a few of them below.
Blogger
Blogger is a free blogging service owned by google. It is a very simple service to use and it allows you a rather high level of control over the layout of your blog. Blogger allow you to keep however many blogs you want. They do not accept spam blogs and they will shut your blog down if they feel that it spammy. This can be a problem for blogs with a commercial intent as valuable content based blogs with adds and affiliate links sometimes get flagged as spam and removed even though they shouldn’t be. It can in these cases be hard to get you blog reinstated. Blogger also have a small problem with the fact that page rank don´t bleed to inner pages very well. Blogger is all in all a good alternative for a personal blog but would not be my first choice for a commercial blog. Blogger is only available as a blog hosting tool. You can not download the script to self host the blog.
WordPress
WordPress is the worlds most popular blogging tool. It is available both as a free hosted blog and as a script that you can download and host on your own. Hosting your own worspress installation gives you more control over different aspects but a blog hosted at wordpress.com is also a good blogging option and it is possible to host your blog on wordpress.com while still using your own domain name as the address. WordPress has a huge fan and developer base. You can there fore find a very large number of different plug ins, addons and themes for wordpress allowing you to modify you blog into almost anything you would like. You can among other things turn it into an e-commerce store with a shopping cart system, a real estate site, a coupon site and a lot of different other things. You need to use self hosted wordpress to be able to use all of these plug ins as they are not available on wordpress.com.
WordPress is the tool I recommend for everyone who wants to get started in the make money online niche.
WordPress network/MU sites.
These are sites that uses the same or similar software to wordpress.com but that are unassociated with wordpress.com and ran by other companies or individuals. Although you get mostly the same features as you do wit wordpress.com I still recommend that you stay away from these sites as you will never know how long they will be around or if the owner will give you ample time to move your blog before he discontinues the service if he choices to do so. There are a lot of these smaller services that are reliable but unless you know for sure that the one you want to use is one of them than you are best just going with wordpress.com which you know will be there tomorrow and that offer the same or better features.
Typepad
Typepad is a somewhat popular free blog hosting service. Typepad is best for diary type blogs and small personal blogs. I can not recommend typepad to anyone who want to start their online career. It can however be a useful source for links as the blogs are indexed and free.
Squidoo
Squidoo is not as much a blog host as it is a place where you can publish individual pages about a certain topic. Squidoo can be good to snipe individual keywords and can be used for making money but is not a suitable solution to start your business on. Squidoo can be good for building links.
Hubpages
More or less the same as I said about squidoo goes for hub pages as well.
Live journal
Live journal is a blogging platform that as the name might suggest is most suitable for keeping journals of different things. It is no where near as good as wordpress and not suitable for those who want to start making money online. It can however once again be used to build links.
There are other platforms available out there as well but the ones mention above are among the most commonly used.