This is a very old question, but I do not feel that the benefits of ASMX have been fairly portrayed. While not terribly flexible, ASMX web services are very simple to use and understand. While WCF is more flexible, it is also more complex to stand up and configure.
ASMX web services are ready to stand up and add as a webservice reference as soon as you add the file. (assuming your project builds)
For the simple development workflow of
create webservice
-> run webservice
-> add webservice reference
, an ASMX webservice has very little that can go wrong, not much that you can misconfigure, and that is it's strength.
In response to those that assert that WCF replaces ASMX, I would reply that WCF would need to add a streamlined K.I.S.S. configuration mode in order to completely replace ASMX.
Example web.config for an ASMX webservice:
<?xml version="1.0" encoding="utf-8"?>
<configuration>
<appSettings />
<system.web>
<compilation targetFramework="4.5" />
<httpRuntime targetFramework="4.5" />
</system.web>
</configuration>