The old ASMX web service technology is still supported, but is nearing end of life. See Microsoft: ASMX Web Services are a “Legacy Technology”. In my opinion, this makes it unsuitable for production use, unless there’s no other choice.
There are a few other Microsoft web service technologies I will mention only to warn you away from. They are obsolete and should not be used for new development. In fact, anyone using the following technologies should migrate to WCF as soon as possible.
Web Service Enhancements, or WSE were a set of stopgap releases that added to the ASMX technology to permit developers to work with the emerging WS-* standards as they were being developed by the industry. That means you will often find WSE mentioned in conjunction with security. This does not mean that WSE is the solution to security in web services, it means that WSE was that solution until WCF was released. WCF supersedes WSE, which is now obsolete.
Even more obsolete is the SOAP Toolkit. This was a way to create clients for web services, and worked for old VB or ASP applications. Do not use it.