As a web-based business, do we need to register as a foreign qualified LLC in every state?
The answer depended on a number of factors including whether there were a minimum level of contacts with a particular state or court that made it fair for it to hear the case (as opposed to a different location). The same thing happens with business registration.
The threshold question is whether you have enough "contact" with states outside of Texas to require that you register your company in those states.
What is considered contact? Outside of having a physical office within the state, this can include making regular business trips into the state, repeatedly soliciting for clients within the state (as in a directed advertising campaign), and actually performing services within the state.
It would be wise to speak with an attorney about the exact nature of the services you provide in the other states, as these kinds of jurisdiction issues are determined on a case-by-case basis.
Also speak to your accountant--just because you don't have to register as an entity in the other states, that doesn't mean that you wouldn't have to pay taxes on income derived from those states.