Alternate approaches would be to use another framework entirely (such as Ruby on Rails, some form of PHP, etc.), however since you're familiar with ASP.NET, I'd say to give MVC a try. It still uses the .NET Framework and Feature set, just with a more logically conceived toolset to interact with when it comes to the web.
All of this goes out of the window if the application you are making is small-scale, such as for a company intranet servicing dozens of employees. In that case, the speed and simplicity of Webforms might be exactly what you're looking for - though you'll find that, as mentioned above, doing much in the way of consuming web methods and updating partial pages will be an onerous chore.
For variety, here's a couple of contrasting views: