Major operators in Germany are T-Mobile, Vodafone and E-Plus/O2. (http://gsmmap.org)
 Purchasing a prepaid SIM in Germany
See http://prepaid-data-sim-card.wikia.com/wiki/Germany#Survey_of_MVNOs as well for up-to-date information.
Please notice that registration/activation is mandatory in Germany. This usually includes specifying your name and a valid (but not necessarily verified) german address. In most cases, a hotel or hostel address should work as well. If you can, ask the place you buy the SIM card to activate it for you directly.
In general, several supermarket chains (including Aldi, DM and Norma) sell SIM cards for their own mobile servies, but they need to be activated online afterwards, which might be difficult because one has to be online on the one hand and the website are frequently only in german on the other hand.
One service that has an english website and seems to get recommended frequently for international travelers is Blauworld (http://blauworld.de/index-locale=en.php). For roughly 10 EUR, you can get a SIM including 7,50 EUR of credits.
 Nano SIMs
If your phone requires a Nano SIM card, take special care as lots of prepaid SIMs you can buy in supermarkets and gas stations are not Nano size. One can usually order a Nano SIM online.
 Purchasing Credits
It is in general possible to buy add-on credits in supermarkets or gas stations for your prepaid provider. You get a number code you can transmit via e.g. SMS and they will recharge your credits.
 Data Plans
Regular internet usage with a prepaid SIM is quite expensive, as they charge by the data (e.g. 0,50 EUR per MB in the case of Blauworld). It makes sense to activate a time-based data plan, even though most of them are for 30 days and you might not be in Germany that long. Make sure that the data is only throttled and not deactivated once you run out of high-speed data (usually to GPRS speeds, i.e. 56 Kbits/s) so that you do not have to pay the high feed per data again.
It is recommended to switch off packet internet before you insert the new SIM and until you got a confirmation that your data plan is active, otherwise your phone might download data on an expensive plan.
 Purchasing SIM cards at airports
This data is compiled via internet searches, so please update it if you have first hand knowledge after arrival.
It should be possible to buy SIM cards at both Frankfurt (FRA) and Berlin-Tegel (TXL) airports.
People seem to recommended http://www.frankfurt-airport.com/content/frankfurt_airport/en/shop_enjoy0/shops/photo_electronics/photair.html in Frankfurt, but the airport is big enough that there should be other places as well.
Berlin-Tegel is much smaller, but according to this Tripadvisor thread (from 2012) there might be a branch of the "Reisebank" bank which sells Blauworld SIM cards. Another thread mentions a store called "capi" across the information desk.
 FRA Airport
The O2 store outside of Terminal 1 Hall B (arrivals) next to the postal services and information desk say they don't stock prepaid SIM cards. The postal service counter in the same shop area says the O2 store opens around 08:00-08:30. It opened at 08:20 when I was there.
In terminal 1 Hall A there is a Nokia store with "Prepaid" on the sign, this store opens 09:00. They sell Turkcel packages. The cost of a 5G prepaid SIM is 50 EUR, the guy activated mine while I was there. I plugged it in my notebook at the hostel and has UMTS/HSPA connectivity. http://www.speedtest.net/my-result/4564012163.
 Roaming from Other Countries
 Roaming from UK mobile networks
On PAYG tariff: £1.99/day for O2 Travel bolt-on (for 50MB/day); 19p per MB without.
On PAYG tariff: varies from 19p per MB, to £3/day (for 100MB).
On Pay Monthly tariff: 19p per MB, or £3/day for EuroTraveller
Requires a Euro roaming data add-on, £12/week (for 200MB/week), £24/week (for 500MB/week), or other options.
£5/day for Euro Pass, or 19.8 per MB without. (Germany is not a "feel at home" country.)
 Roaming from Egypt mobile networks
Etisalat has a couple of roaming offers that ends on Sep 1st, 2015. The offers includes Germany. Pre/post-paid & corporate customers are eligible to benefit from this offer.
 Flat rate offer
- Flat rate of 1 EGP/unit for all outgoing, incoming voice calls & SMS
- No capping on the minutes/SMS to be consumed
- Customer will opt-in once and enjoy the offer till end date of the offer
- Flat rate offer including Mobile Terminating, Mobile Originating & SMS and excluding Mobile Internet
- Opt in through sending an empty SMS to 135 with normal SMS fees or through USSD *135# free of charge
 Weekly bundle
- 400 EGP/week
- No capping on the outgoing minutes / SMS to be consumed, and MB will throttle after 125 MB
- For incoming calls fair usage policy of 200 minutes will be applied, after that customer will be charged with normal rates
- Bundle validity 1 week after the week customer can re-opt-in again or enjoy the normal rates
- Opt-in through sending an empty SMS to 136 with normal SMS fees or through USSD *136# free of charge
- Full bundle fees will be deducted once customer subscribes to the offer
- Opt in through sending an empty SMS to 136 or through USSD *136#