Your U.S.-based T-Mobile HotSpot account gains you access to the German T-Mobile Hot-Spots on a roaming basis - the charge is USD 0.18 per minute. You simply indicate that you are a T-Mobile U.S. customer, then, after agreeing to the roaming charges, you are instantly online. You are billed on your next billing date (no need to enter any credit card information.
If your hotel uses T-Mobile as its wireless provider, you may also be able to buy a 24-hour unlimited pass. It's not cheap (it was €18,- in November 2006, the last time I had need to use it) but it may be useful if you have one specific day that you need a lot of access time.
What I usually do is, I compose e-mails off line in my hotel room, then go to the HotSpot (a Starbucks, for instance, or maybe the Hauptbahnhof, some of whose home pages have a link to T-Mobile's roaming page) and conduct my online business (such as anything financial, online check-in for flights, etc).
If I want to just surf generic sites (like reading FlyerTalk, for instance)
, I find an Internet Cafe for that - USD 3.00 per hour is better than USD 10.80 for things that you don't need the security of your own laptop for.