A couple of months back, Google added the option to import email accounts to your Gmail address - all messages and contacts. However, because it was a tool for switching to the service, it was limited to new accounts.
Now, Google's opened the functionality up to anyone who's got an old spam-clogged Hotmail account that they never check. To get all that info into your Gmail, goto Settings > Accounts & Import and hit "Import mail and contacts".
You also have the option to forward any new mail your old account gets automatically for 30 days. Beyond that, there's always the option to set a manual auto-forward yourself. The copying process takes between a couple of days and a week.