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 web hosting companies that accept monthly payments:
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 if you choose to pay month to month.
Hostgator has monthly payment options on all three of its shared hosting plans: the smallest Hatchling Plan which supports hosting of just one website, unlimited storage and bandwidth for $10.95/month, the Baby Plan which allows hosting of multiple (unlimited) websites on a single account and also includes unlimited storage and bandwidth for $11.95/month, and the Business Plan which adds Free Dedicated IP and Free Private SSL for ($16.95/month). 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 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.