In short I want to start developing web related apps that people can easily 'plug-in' to their own site (like a Chat, Video Streaming, MP3 Player).
What would be a good language for doing this?
Otherwise I'd say Silverlight or Flash.
Silverlight is great if you are a .NET Developer, but it requires a plugin and isn't as widely adopted. It also has the negative connotations associated with MSFT. There is also Moonlight by the studs behind Mono, which gives you an open source option for development.
Flash is the standard for "rich" content, but with HTML5, Flash is finding increased competition. It's good, but does require proprietary toolchain to build flash apps.
On the server-side: Server-side logic can be supplied with java which is typically readily or easily available on most hosts. It can also be supplied with most any language/framework (ASP.NET, Struts, PHP...) that you believe "your" 3rd party sites will support. If you stay with GWT for the server side, you're "all set", if you use other languages, you'll just need to ensure that you can read/write json messages and hook in a relatively simple RPC framework.
(1) I'm only familiar with GWT, but I know MSFT has (or had?) Volta. I wouldn't be surprised if many similar tools were readily available or were to show-up shortly.