Most web hosting companies require that you pay for at least one year of hosting upfront. It's harder to find those that allow you to pay month to month. These are the web hosting companies that accept monthly payments:

Godaddy Monthly

GoDaddy

Godaddy offers monthly payment options on two of its hosting plans: the Deluxe Hosting plan which includes unlimited websites, storage and bandwidth for $10.99/month when paid monthly, and the Ultimate Hosting Plan which adds twice the processing power and memory (Linux with cPanel only), Premium DNS and 1 year SSL certificate for $16.99/month.

New! Godaddy has a great deal today (Wednesday, October 18th): 12 months of Economy Web Hosting for just $1/month.

HostGator Monthly

HostGator

HostGator offers a monthly payment options on all three of its shared hosting plans: Hatchling Plan ($8.95/month), Baby Plan ($9.95/month) and Unlimited Plan ($14.95/month). The Hatchling plan supports only a single website, while the Baby plan allows hosting of multiple (unlimited) websites on a single account. You can get the first month of hosting for just 1 cent by using the coupon code 1cent or just use their default 20% discount code if you want to pay yearly.

DigitalOcean Sq

DigitalOcean

DigitalOcean is one of the best VPS hosts. It has plans starting from $5/month for 20GB of SSD storage and 512MB of RAM. A Virtual Private Server doesn't come with a control panel, web builder, Wordpress or any other software you get with shared hosting. It is a lot harder to setup than a standard shared hosting. You have to install your own Linux distribution, setup the web server and any other software you need. This is only for advanced users.