What are the speed limits in German roads?

I heared that there is no speed limit in there autobahns. Is that still valid? What are the speed limits (in general) in German roads? Like with in city limits, urban limits, minor road, major roads, etc.

What shall be considered to be a decent speed in Autobhans, since there is no speed limits?

50 within city limits, 100 outside, none on the autobahn (all in km/h), but mind that there are many speed limit zones (white round sign with red border and a black number, indicating the limit in km/h), also on autobahns. A decent speed on the autobahn, in my opinion (I'm German) should be something between 140 and 160 km/h.

Mind that on minor roads, you won't find many speed limit signs (so you're theoretically allowed to drive 100), but rather signs warning you of sharp bends etc. You're expected to adapt your speed accordingly.

While it's true that you are not going to find many signs telling you the speed limit for out-of-city/not-autobahn, and you are supposed to adapt your speed to the road and your own abilities, they'll still give you a speeding ticket if you're going faster than 100km/h and they catch you at it. (grrrrrrrrrr......)
And they can also fine you for a lot of different things here. Using your mobile phone is forbidden, taking over on the right hand side is forbidden, there's no turn on red (unless they hung up a little green arrow, which most of the drivers have no clue about, and than you stand there, know you're allowed to turn when noone's coming, but the lovely driver in front of you is standing there like someone glued him to the spot and wont budge!)

Also, there's a law that says that "autobahnlike" streets have no speed limit. Autobahnlike streets are four-laned streets that have a green (with plants and grass and stuff) stripe sitting between the two directions.

A good sped limit, I think, would be something like 150km/h.

Within city limit it's 50kmh (unless indicated to be slower), on roads outside city limits it's normally 100kmh (unless indicated), and no speed limit on the autobahn (unless indicated).
But as Alwin already mentioned, best speed on the autobahn to keep the traffic liquid is around130kmh. 180kmh is ok when the autobahn is free and dry with no strong sidewinds. A great feeling.

There's no speed limit on the germans' Motorways

In general you have no speed limits on a highway. Partly they are restricted in areas with high accidents aggregation (around 120).
The minimum speed on highways is 50, below this you are not allowed to enter a highway. The recommended speed is 130 (only a recommendation), which is normal on a two line highway. But in general you have no limitation (so if you want to drive 250 you can do this).
In the city you have normally 50 as normal limit (can depend on the street you use, also 5 or 30 is possible) or higher (for special streets.
Outside 100 is normal, except special streets which are not normal Interstates. They can also allow more.

Usually i am sick of it just refering to Wikipedia but in this case their aricle is great:
http://en.wikipedia.org/wiki/Autobahn

there is no speed limit on the autobahn, but there might be if there are repairs....

First there are only SOME areas of the autobahns that have unlimited. Much of them have speed limits though still faster than most places in the USA say an average of about 90 mph roughly give or take I saw a lot on A4 Autobahn.

I am told areas in Bavaria there are some unlimited areas where you can go as fast as you want.

Just because you do not see cops on the road you can still get a ticket. They are well known for electronic digital photos of your liscence, the drivers face and the speed they were going so they just mail you the ticket. Too many and you lose it.

In the cities and towns there are definately limits and some roads are very narrow so watch out. Also learn the rules of their roads, they are a bit different than the USA, like you cannot turn right on red or be eating your McDonalds meal and talking on you cell phone while brushing your hair and changing the CD. Driving is taking far more serious there in my opinion. DO NOT drive on the left unless you are passing and NEVER pass on the Right!

Hope that helps and to be safe get an international liscence to prevent any problems with the police possibly.