I had to close my hotmail account as well a few months back it got hacked and was sending spam emails - namely to my boss with this msg that I was starting my own business with this chinese company. It got to the point that I had to get our IT people to block my email account from sending emails to the office. Thankfully I've never had any issues with my gmail account. I have two virus softwares running as well and they're always popping up with issues that it finds with websites and stuff coming in.
When I contacted Hotmail about the SPAM and the issues with the account being hacked their response was it must have been a site I went to, and that to close the account for me to not login to the Hotmail account for a period of 60 days and it will automatically remove the account. So for 60 days my family and co-workers got spammed every day.