Summary: Windows Live Hotmail will typically show you the date your Windows Live account was created - even if it was created before Windows Live existed.
I want to know the year I signed in with my e-mail address: ****@hotmail.com.
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I'm going to assume you mean what year you first signed in. The history of other sign-ins, including the most recent, is to the best of my knowledge not available.
However, the date you created your account may well be.
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Here's what I did to get mine:
After signing in to the full version of Windows Live Hotmail, click on the Options link in the upper right of the window:

That presents a drop-down list, at the bottom of which is the More options... link. Click on that and you'll be taken to a page that includes, in part this:
Click on View and Edit Personal Information and you'll reach your destination:
Here you can see I've had my account since 1999, not long after Microsoft acquired Hotmail. (I blur my Hotmail address because it's most definitely not the way to contact me.)
You should be able to follow these steps and get similar information about your own account.
One caveat: since your account may be used for multiple services such as Hotmail, MSN Instant Messenger the date would be the date you created the account, regardless of which service you first used to create it. Thus, if you create the account to use MSN Instant Messenger, and then a year later start using Hotmail with the same address, the date shown would be the earlier of the two.
Related:
Ask Leo! - Can I check when my last Hotmail login was?
Ask Leo! - MSN Hotmail: how long will Hotmail keep my account open?
Article C3430 - June 29, 2008
Leo's directions are correct, if MSN is not having problems! I'm using Firefox and when I followed the directions I couldn't get to the account info screen. So just to see I logged on to IE (which took so long it confirmed my Firefox preference once again), and there I got to the account info. Back to Firefox and this time it worked.
Posted by: David R Heym at July 1, 2008 10:46 AMThanks Leo, I always wondered just how long I had been a member. Not really imortant information but good to store in my brains filing cabinet.
Posted by: Don Smith at July 1, 2008 2:59 PMJust go to https://account.live.com and sign-in it will provide you with all your hotmail/live information.
Posted by: KaZuYa_X at July 1, 2008 9:00 PMI want to know how do I check/find out when my friend created his account? how do I do that?
Posted by: Nas at November 20, 2008 4:06 AMI just did this, and what's weird was, while I distinctly remember having registered my present hotmail account by at least mid 2001, when I looked at the personal info page it said that I had only been registered since August 2004. The only reason I can think that it would say this would be because somewhere around that time frame I simply quit using hotmail for a long enough period of time that they disabled my account, and so whenever I tried to log in again and had to reactivate everything, they must've simply switched forward to that date as my official registration date.
This is quite the disappointment though as now I have no way of knowing precisely when I started using that address.
Posted by: Bill at January 14, 2009 8:15 AMyou cannot receive or send a message before your regristration date.
Posted by: dhiren roy at February 28, 2009 3:22 AM