I had replied to one of the posts on an online forum sites which had a simple question. However, looking at the upvote count by different users shows that there’re many who had similar question. Thus, I decided to create a blog post on the same,
Question: Why Asp.Net Web Service Application template is missing in Visual Studio 2010?
Solution: ASP.NET Web Service Application project template is not available for .Net framework 4.0, however, available for .Net Framework 3.5.
If it’s a new development targeting .Net framework 4.0, you can chose WCF Service over ASMX web service as ASMX web service is legacy. Please note that you'd need to enable AspNetCompatibilityMode to access HttpContext objects.
If you still want to use classic ASMX web service, choose ASP.NET Empty Web application and then you can add ASMX webservice files to the project.
Hope this helps to save some time!