You've fallen for the Microsoft trap of "it's just about web services" :-)
It's actually a lot more:
- it's about service-oriented programming in general (not just web services - you can also write TCP/IP based services, MSMQ queue-based messaging and a lot more)
- it's about unifying all the diverse programming models that existed so far (ASMX, Enterprise Services, DCOM, .NET remoting)
- it's about providing a lot of ready-made and ready-to-use plumbing which can handle things like reliable messaging, transaction support, security in any shape or form you'd like, service discovery, and a lot more
- it's about separating the service implementation from the details of how clients will call it and making this a configurable stack of protocols, encodings etc.
Sure - most of this stuff can be done in ASMX, or .NET remoting - but try to convert an ASMX web service to be callable in your intranet using TCP/IP and transport security... Many of those "older" technologies have a very intricate and direct link to how they're being used - you can't easily change that without changing the whole service code.
WCF separates all these "plumbing details" like what endpoint to call, what protocol to use to call it, how to handle security etc. out into a "WCF stack" that's configurable and composable, so you can easily switch your service XYZ to use HTTP allowing anonymous users to call it, to using TCP/IP with Windows credentials required - your service code won't change a bit - it's only configuration of the plumbing.
That to me is the most compelling reason for WCF - I can totally concentrate on my actual service code, and not pollute it with lots of plumbing stuff - how to handle transports and text encodings and all that. And I can easily change that and adapt to new requirements and needs in deployment without having to touch my actual service code.
Plus, the second major point is extensibility - most of the older technologies just had their one, set way of doing things and many didn't lend themselves to being extended. You had to either adapt to use it the way they did it - or forget about it. WCF has a vast and very intricate system for extending just about anything - you can create your own transport protocol (people have created UDP or SMTP based bindings), you can create your own message encoders (like I had to do to talk to a web service which could only understand ISO-8859-1 encoded messages), and you can extend just about anything else in WCF - all in an organized, well-documented, very stable and safe way.
So these two things - separating out plumbing into configurable layers, and extensibility to the maximum - are the most compelling reasons for me to use WCF.