Canadian Web based Company doing business in US
You will have no problem registering your U.S. business as a Canadian citizen. We have a research article dedicated to international entrepreneurs looking to open a U.S. company titled 'U.S. Companies for Foreigners'. This will guide you through the online application process, as well as compare the different entity types you could register and recommended states.
Since yours will be a web-based business, you would be able to register the company in one state, such as Wyoming, Nevada or Delaware, and conduct business with customers/companies located in other states without a problem. For example, you could have a company registered in Wyoming, and someone in California can order your products/services directly from your company's website, without you needing to be registered in California.
Had you planned to conduct a physical business, such as having an office, employees, property, etc. in various states, then you would need to file your company as a foreign entity in each state with physical presence.