That's possible because of Windows Live Messenger IM Control & Presence API.
Now how to put this control on your site or Blog, check out the steps:
-Go to Messenger Web settings page, http://settings.messenger.live.com/applications/websettings.aspx and sign in with your Windows Live ID, to get the setup page as shown. Select "Allow anyone on the Internet to see my online status and send me messages" checkbox and save.
-Next click on 'Create HTML' to get this. You can choose the control you wish to put on your blog. Here we want to put the Messenger Box, so we will choose Messenger.
Actually its displaying the status realtime, if you are signed into Windows Live Messenger, it'll show its status as online.
- It''l l generate the code according to the control chosen.
So this is the code which you will copy and paste into your Blog or Site. That's all. The only change I made to the code is reduced the 'width' to accommodate in my blog.
Note: When you use HTML to show your Messenger status, people can copy the HTML and show your status elsewhere on the Web.
So when a visitor comes to your Blog, he can click on 'Begin Conversation' to send IM to you.
Now, we can test it too.
The IM Control lets anybody on the Web IM you. You cannot IM yourself from the Web, but can test IM as a Visitor.
If somebody you don’t know sends you a message, you"ll see a warning in Messenger.
Now something more about this control,
"The Windows Live™ Messenger IM Control lets people on the Web reach you in Messenger by showing your Messenger status on your web site, blog, or social networking profile. The IM Control runs in the browser and lets site visitors message you without installing Messenger first. It is supported in IE6, IE7, and FireFox 2.0 on Windows and FireFox 2.0 on Mac OS and supports 32 languages.The Windows Live™ Messenger Presence API is a JSON API which returns a users status & display name, this can be queried programmatically."(Angus Logan Blog)
"The IM Control is a HTML widget that allows a user to publish their Windows Live Messenger presence and provides two way conversation from a web page to a Messenger client. The control allows anonymous users to see presence and send messages."(viawindoslive)
In my view , it'll be a very useful in cases where some visitor on my blog expects a reply by mail to a particular post or in the comments box and waits for it. While using this control, if online, one can have direct discussion.
Also check the Angus Logan Blog where this announcement was made.
Now I can see already being put in many blogs as Via Windows Live
UPDATE: I just now tried the displaying the 'Status icon' instead of the 'Messenger'. I used it in signature in a Forum. So if one clicks on the Status icon, the Web messenger opens up in new page in the browser and one can have conversation. So for those who don't want to display the Messenger box can make use of 'Status icon' which when clicked will open up the Web Messenger box.