mitfahrgelegenheit.de and mitfahrzentrale.de are popular commercial websites for carpooling. However, since they started charging a certain percentage for each ride they mediate, there are new pages starting to be used more and more. Some of them are: bessermitfahren.de; blablacar.de.
Germany is one of the easiest countries for hitchhiking.
The country has an expensive railway network. As an alternative to the standard fare, you may also check offers and sales, for example regional or seasonal tickets.  If travelling in a weekend it is possible to buy a ticket valid for unlimited travel for one day on all regional trains for up to 5 persons. See  See also Deutsche Bahn.
Bahn.de is quite expensive. Sometimes it makes a lot of sense to get a 25% reduction Bahncard simultaneously while buying a ticket as you can earn back the cost of the card with just 1 ticket already. Just make sure you cancel the Bahncard right after you get it, otherwise your stuck to a yearly subscription.
You can try to "hitch" group tickets in the weekend, as more people are traveling with tickets that allow up to 5 people to travel with just one ticket. However, this has gotten more difficult recently, as the Deutsche Bahn started to require everyone's name written down on the ticket. They might check for IDs to see if you're actually the person whose name is on the ticket but they barely do it.
Ltur often has good "last minute" deals that, from 26 euro within Germany (book between 1 and 7 days ahead) and 36 euro abroad (book between 3 and 14 days ahead).
In general, it is quite easy to take trains without a ticket but the legal consequences are worse than in most countries if you get caught. "Obtaining services under false pretenses" is a criminal offense with a one year prison sentence as a maximum penalty. Depending on the tricks you use, you might also be charged with fraud. However, you will usually just be issued a fine by the train company (60€ or the double amount of the ticket price, depending on which is more) and if you pay it and you don't get caught more than three times, you probably won't be criminally charged at all. Ask local people for good tricks, there are proper ways of taking pretty much every train without a ticket.
There are some relatively new low budget bus options available:
busradar.com is a great website for comparing prices of long-distance buses, trains and ride shares.
mitfahrgelegenheit.de once was the most popular website for carpooling. Since they started charging a certain percentage for each ride from the drivers, there are new pages starting to be used more and more. Some of them are: blablacar.de and bessermitfahren.de.
- Bus: ADAC Postbus, BerlinLinienBus, Busbud, Flibco, MeinFernbus, Orange ways, PolskiBus, Simple Express
one important keyword for alternative life in Germany and in general in German speaking countries is "Wagenplatz" (also called "Wagenburg" or "Wagendorf"), which is sort of a little village out of wagons, vans or other wicked vehicles where people live. Every Wagenplatz is different and there are some more secluded than others, but they are usually keen on helping like-minded travelers. Also some of them in the cities use to hold "Volksküche" in the summer as well as many other events. They use to be very engaged with the alternative scene. You can find a list of them here (although not complete and unfortunately in German): http://www.wagendorf.de/index.php/Links#Wagenpl.C3.A4tze
Wild camping is generally prohibited in Germany, but is barely monitored. If you don't raise too much attention, you will be fine.
In nearly every town there are alternative centres where people cook for everybody. The price for a warm dish is between zero and 2 Euro. Have a look at the list here. (German)
In many german cities you can find so called "Voküs" (or Küfa = Küche für alle, kitch for all) which is short for "Volxküche" (peoples kitchen). There you can eat for free or donation. Ask for Voküs in Squats, social centers or other alternative places. Here you find a list of vegan Voküs: http://de.veganwiki.org/vegane_vokue
Also dumpster diving works pretty well all over Germany, but watch out for cops, while you do it, they might cause you problems. Try to get to the supermarkets when they already have been closed for at least an hour. Otherwise, it's quite likely to be spotted by workers. They will usually just chase you away if they see you for the first time but they also might call the cops. Dumpster diving is considered theft in Germany. For many dumster diving spots, you'll have to climb over a gate or a fence so you can be charged with trespassing as well. If the dumpster is accessible without any barriers, it's not considered trespassing (unless you don't leave the property if a worker tells you to do so).
In Germany and Austria you can enter places like Burger King and go to the holder where people leave their trays. You can stuff your face with all the fries you'll ever want.
Drinking tap water is safe all over the country. You can usually get inexpensive but good food at Italian and Turkish takeaways, the latter ones have Döner or Kebap written on them. Typical German fast food shops are marked with Imbiss signs and sell cheap sausages and French fries. Keep in mind that most shops including some supermarkets close at 20:00 and on Sundays, although many supermarkets might be open until 22:00 during weekdays. Petrol stations, 24-h shops and kiosks have a very limited food choice and are more expensive. As a free alternative you can try dumpster diving. More information on this can be found in the trashwiki article on Germany.
Even on every big railway station you can find Bahnhof Mission. This is charity Christian organisation that can help you in different needs. Don't abuse them so much because mostly it's for homeless people but if you need feel free to come. They can give you advices where you can find free food or free place to sleep, because they know all charity organisations that operates in the city. You can make a call from their phones, charge your devices, have rest in their room, warm yourself in the cold period. Sometimes they have some food (usually sandwiches) and free tea/coffee. They do not allow to leave your luggage. Usually they open 24 hours with some breaks for cleaning during the day. Sometimes you can stay there for a night, you can put your sleeping bag on the floor (but it depends of the workers), it's not the mandatory.
Eating on the Autobahn
Try to avoid eating on autobahn service stations if you want to save money and if have a good taste of food. These restaurants are notoriously expensive and the food quality is quite low. If you're lucky you can find thrown away Sanifair vouchers of the toilet system. You get a cumulative 0.50 euro rebate for them in the shop.
Blau.de is a good deal. Aldi could be cheaper but has fewer options to add credit.
Busking generally works great in Germany, especially in medium-sized towns. People tend to appreciate what you are doing and if you busk with a group, it's quite common to have a crowd gathering around you. Laws differ from town to town and are quite different. In many places, busking is legal but restricted in terms of duration, spots, time of the day etc. In some places, you will need a permission. Usually, you will be fine no matter if you pay attention to the laws or not. You might be sent away by "Ordnungsamt"-officers (something like police for minor offenses). Sometimes, you will get a fine. If you don't care about what they told you and continue playing music, they might seize your instruments or call the cops.
Germany is part of the Schengen area which means that borders with other Schengen countries are open. Since 2009, all neighbouring countries are Schengen members as well, so there are no fixed border controls any more. At times, there are mobile checks by the police or customs, especially in border regions or on the Autobahn.
At the Swiss border, there are still custom controls, but that will probably only affect you if you are on a truck.
Update January 2016
Because of the refugee crisis in Europe some countries have reintroduced border controls. In Germany this will especially affect the borders with Austria and Denmark. Prepare for traffic jams at the border and keep your passport ready.
Augsburg, Berlin, Bielefeld, Bremen, Cologne, Dortmund, Dresden, Düsseldorf, Erlangen, Frankfurt am Main, Freiburg im Breisgau, Hamburg, Hannover, Karlsruhe, Leipzig, Munich, München, Münster, Nürnberg, Osnabrück, Rostock, Salzwedel, Stuttgart, Ulm, Witzenhausen
Apollo-NG, Basislager Coworking, Bona-Peiser-Bibliothek, Dezentrale, FREIraum in Bad Hersfeld, Kesselberg, KuBiZ Weißensee, Kuckucksmühle, MS Stubnitz, OpenEcoLab Rahden, Projektwerkstatt Saasen, React!OR, Systemfehler, Teepeeland, Traumschule, Trial and error, WAA Düren, Yunity
In Germany there are shops where you can bring unused clothes in a good state and/or take new clothes home. It does not cost anything. A list of these shops is available here. (German)
Most toilets on the service stations are maintained by Sanifair and are clean. You get a 0.50 euro coupon as part of the 0.70 euro service fee, which you can redeem when buying things at the petrol station shop or in the restaurant. Pathofdhamma suggest to seize the moment and jump the barrier if there are no people or cameras around. The turnstyle is only blocked for the inwards direction. With some luck and smooth moves, you can sneak in. Turn it towards you, walk one step; turn it again, walk another step: you are in!
There are showers in most Raststätte and Autohof service stations on and near the autobahn. Prices are between 2 euro and 5 euro.