And the reality is
the most of the good offers in the 5-6% range are with severe conditions (see below). Mostly you need to invest a % of the money into their fonds services to get this.
If you don't want to do the funds you usualy only get 2% to 3%.
But if you are interested, here a short translation (had some time on hand and need to keep my german skills alive).
However please note they also have DIRT that get's deducted and opening an account via mail is not always possible. Also they have an even strikter money laundry law and all accounts can get reported to the Finanzamt (Revenue).
1822direkt „ZinsInvest“
6% if you take 5000 Euro for 3 month but you have to invest 50% in their fonds
Bankhaus August Lenz „Konto Classic Plus“
2.75% for funds over 1500 Euro (even if you are at 1501 you only get that on 1 Euro) and only for 4 month period.
BMW Bank „Spar&Invest“
50% needs to go to a fund and the rest get's 6% with a minium of 3000 Euro to invest
CC-Bank „Geld-Management-Konto“
2.75% up to 50,000 Euro, over that only 2.25
But no fonds investment needed
Comdirect „Best of all“
only for new customers - 2.6% up to 50,000 Euro
Comdirect „fest & fonds“
Again 50% goes to fonds and the rest gets 5% however it's fixed for 6 month and requires 3000 minimum
CortalConsors „4foryou“
You need to buy shares on any company for 4000 euro via them and then you get 4% on you other funds up to 10000 euro and your depot of shares value can not go below 3000
DaimlerChrysler Bank „Tagesgeldkonto“
2.45% (no fonds needed) for up to 100 000
DHB „NetSp@r-Konto“
2.75% however this is a dutch bank and only up to 20000 Euro are guaranteed in case of a bank failure
Diba „Extrakonto“
2.5% on all funds (however interest is only going to the account once a year).
Dresdner Bank „SuperPlus“
Again only with fonds and than you must invest a minimum of 10000 and 60% to the fond. 5.55 on the money that is not on the fond.
Ethikbank „zwEI komma neun“
2.9% for a maximum of 20000 (no fonds needed)
Netbank „fifty-fifty“
Again fonds needed (50%), rest gets 8 however the t/c are very restrictive.
Postbank „Sparcard 3000 direkt“
A minimum of 3000 Euro needed, than you get 3%. Your funds can be accessed via a VISA ATM card
Volkswagen Bank „Plus Konto“
2.5 % if you invest more than 100000 below that a complicated table of rates down to 2.25%. And you get 25 Euro of Aral tank vouchers.