How can I get a me.com e-mail address? Was this a service only offered with Apple's Mobile Me? Is there anyway I can still get an e-mail address ending in @me.com?
It's basically not possible to make a new MobileMe account while the transition to iCloud is happening. There are some loopholes (like adding a new account under an existing Family account) - but most will have to wait until iCloud is released. The official word on that is a vague - in the fall of 2011.
From the Apple preview page covering Contacts, Calendar and Mail as part of iCloud:

Mail that delivers. Free.
When you set up iCloud, you get a free me.com
email account. iCloud automatically
pushes new email messages to all your
devices, so your inbox is up to date
everywhere you check it. And iCloud
keeps all your folders in sync, no
matter which device you’re using.

That was posted June 6, 2011, and I think that's pretty definitive. Free me.com accounts for all. It's unclear if you can get a new one today, but when iCloud opens to the public, you'll be able to sign up for one.
The sign-up page for MobileMe was disabled when iCould was announced at WWDC. People with unredeemed paid memberships can request a refund as they can no longer create a new account. Also, the free trials are suspended - presumably until iCloud opens this fall. The MobileMe transition FAQ documents this in detail and should be updated if things change before iCloud details are released.
The only way to get an account is if you already have a Family Pack with unallocated sub accounts. It is not clear if and how that sub account will transition to iCloud, but that may be an option for some to establish MobileMe email after June 6, 2011 and before iCloud opens for business.