And I just got the Huawei E161 from O2 that Inquisitor mentioned. It was €19 at Saturn. How could I refuse?

Thanks for this informative thread. I am going to Germany for 3 days during the next week and I am bringing my Android Hero with me. During those 3 days, I want to use data ONLY (i.e. no voice calls at all) so I am thinking about buying Vodafone CallYa and using their websessions. However, I don't know German very well so I am not quite clear about some details, even after browsing through vodafone.de site:

a) Can I buy callYa 5/15 SIM card in any Vodafone shop, without being a German citizen, and use it immediately?

b) Does the default callYa price include some amount of credit or not? Can I top up directly in the store, while buying the card?

c) Are all INCOMING calls to this SIM free while I use it in Germany?

Yes, but it would be cheaper to buy a Fonic SIM, since with Vodafone you would need to buy a 7-day-session for € 9.95, while Fonic will charge only € 2.50/day, so for your stay it would only cost € 7.50.
Further with Fonic you can call home to the Czech Republic and to the rest of the EU for just € 0.09/min (landlines) or € 0.29/min (mobiles). Details on Fonic are available at Germany - Fonic - Prepaid Wireless Internet Access
Please be aware, that with Fonic you will need to call customer care and ask them to switch your data tariff to "Tagesflat".

At least those prepaid SIMs offered online come with € 10 of credit. Of course you can add credit in any Vodafone shop or buy vouchers nearly everywhere. For details see Germany - Vodafone Web Sessions - Prepaid Wireless Internet Access

Incoming calls are always free with European operators, as long as you stay in the country your SIM is from.

a)yes

b)yes; yes

c)yes

I bought a German Vodafone SIM in their shop a few years ago, and they registered it at my UK address. To my surprise even the postcode search worked

Thank you, I didn't know about Fonic!

Again, the call-rates are non-issue because I'll really only be using Internet. The more important question is: What is the signal quality of Vodafone vs. Fonic? I'll spend most of those 3 days on the highway or in smaller cities. I don't need FAST internet, I need RELIABLE internet.

Also, I need to use the card as soon as I cross the border from the Czech Republic and buy it in the first larger German city (Dresden, probably). How fast is "switching to Tagesflat"? Don't I have to wait several hours for it to take effect?

I understood that, but I mentioned those call rates as an extra advantage beyond the cheaper data tariff.
O2 also cover nearly 100% of the country and they have EDGE (up to 200 KBit/s) on their whole network, so you should always get a signal and reliable data connections, but Vodafone of course provide better 3G coverage as you can see from this map :

http://www.abload.de/img/o2-vs-vodafonewzqi.png

No problem. All Fonic retailers are listed in my earlier posting. E.g. Fonic is sold at Lidl supermarkets and it can be activated immediately by phone, too.
The switch to the "Tagesflat" is carried out while you are still on the phone with customer care. It's about seconds and you will be notified of the switch by SMS.

Thank you again for excellent info, inquisitor. One last question (hopefully): I'll be entering Germany arounf 21:00 in the evening on Sunday (e.g. most of the shops will be closed). What are the options to buy Fonic? Only Jet gas stations? These are NOT listed on FONIC -- Partnersuche

I'll be entering Germany from Liberec.

I found two Jet gasstations listed for Leipzig:
Jet Tankstelle Dieskaustr 111, 04249 Leipzig
Jet Tankstelle Sommerfelder Str 58, 04299 Leipzig

Notice that the retailer search lists only 6 results per page, you need to click "weiter" below for further results.

But there are also Jet gasstations closer to the border in Bautzen:
Jet Tankstelle Stieberstrasse 49, 02625 Bautzen

I found one in Bautzen, that's closest. Great.

No Fonic SIM cards at Jet!
 

Unfrotunately, the unexpected happened and I had to leave for Germany yesterday evening. I entered Germany after 9 PM and I tried FOUR different Jet gas stations from Bautzen to Dresden. When I asked about Fonic SIM cards, all four cashiers offered me the codes to charge my existing card but neither of them actually sold the SIM cards!

My friend who speaks German very well spoke with them at the counter and they categorically denied they ever sold any SIM cards!

I don't blame Inquisitor because ALL FOUR of these gas stations are listed at fonic.de as sellers of Fonic SIM cards. However, they DO NOT sell them and, according to the cashiers, NEVER SOLD THEM... :(