Summary: Links in HotMail emails are often disabled to protect you. I'll look at how to enable Links in Hotmail, and how to work around it even when not enabled.
Links are not active when I receive an e-mail in Hotmail. How can I unsubscribe to a mailing when the "click here" does not work?
HotMail's trying to protect you.
As you know, there's a lot of bogus email out there that includes links to questionable, if not downright harmful, content. HotMail disables links from senders that it doesn't recognize.
So, the trick of course, is to help HotMail recognize the senders you trust.
Or, if you want to live life on the edge, disable the feature completely.
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Near the top of the message containing the disabled links, you'll probably see a message like this:

Hyperlinks are considered "internet content".
What might not be obvious is that the two statements at the end are click-able:
Enable all message content (once) - click this and the links will be enabled within this message until you close it. So if it's a newsletter you're trying to unsubscribe from (hopefully not mine!), you'd click this, then go click on the unsubscribe link.
Never disable content from this sender - click this and links (and images) from email sent by this sender only will always be enabled. If you subscribe to a newsletter, this is how you might enable its content for this, and subsequent issues.
Now, you can, if you like, turn this feature off completely, but naturally I don't recommend it. Among other things, "internet content" includes images - meaning that items called "bugs" can be included in HTML formatted email that are fetched when you open the email. This can tell the sender that you did, in fact, open the email. In the case of spammers, it tells them that their email has reached a real person and is worth sending even more spam to.
To turn it off, click on the Options link in the upper right of your HotMail screen:

Then click on Mail in the menu on the left:

Click on Mail Display Settings:

The, finally, select the setting you want for Display Internet Content:

Note that for email HotMail considered junk, you'll need to explicitly mark it as "not junk" before links are activated.
With that in mind, there's one more technique that's safer than activating anything, or marking anything you're not totally sure of as "not junk".
For many links, "copy / paste" works well.
Here's a bit of a message displayed in HotMail with the link disabled:

Now, by clicking, holding the mouse button down, and dragging across the URL in that message to select it, I can then right click on the selected link and click on Copy:

Having copied that link to the clipboard, you can now go up to the address bar in Internet Explorer and paste it in:

Resulting in:

In general this copy/paste technique is the safest of all, because it also bypasses any attempts to disguise URLs - links that look like on thing but take you to something else entirely - which is extremely common in phishing scams.
Related:
Ask Leo! - Phishing? What's Phishing?
Ask Leo! - How do I resolve my Hotmail email problems?
Article C2769 - August 25, 2006
dear sir,
Posted by: niraj sherchan at August 31, 2006 6:54 AMi have a problems in my e-mail address is digitalniraj@sherchan.com .problem likes my e-mail works is msn messager but my inbox doesn't work same e-mail address.
i want to make an email address but i do not know what to call it i am asking if you could give me some ideas
Posted by: kylie at September 11, 2006 1:33 AMi have not pc and my job is hard because i have also no time ..........
Posted by: Hamza at September 13, 2006 7:06 AMHamza Memon
Thanks
why website hotmail is forbidden - error 403 ?
Posted by: lama at November 14, 2006 8:45 AMcan you please get bebo unblocked in schools! thanks
Posted by: sarah at December 7, 2006 5:38 AMDear Friend
I was sutpid waking up at ana early morning , I received a messaage from aa friend which has been held in the Junk Emails, but Hotmail asked me if I have to mark it sfe or unsafe , and I clicked on the wrong '' marke as unsfe " And I los he messge , I would like to ge it back ,; is thaat possible ? nad How?
thank you
Posted by: taleb at June 5, 2007 1:28 AM-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
Not possible. Read this article for more:
http://ask-leo.com/messages_deleted_on_hotmail_can_i_get_them_back_somehow.html
Thanks,
Leo
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Posted by: Leo A. Notenboom at June 5, 2007 9:18 AMNXNQ16jimoFJm0LhSPv8BXE=
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In Hotmail Live there is no way to change "mail display settings." How can I activate my links in outgoing messages?
Posted by: John Connell at November 29, 2007 4:52 AMThanks Leo for the most informative and easily understandable computer instructions I've ever seen!
Posted by: D-Rock at November 29, 2007 2:38 PMHELP! I want to make a link with my children, but it keeps rejecting my request!
Posted by: marlin hughes at May 17, 2009 2:28 AM