As already posted, ICE (inter city express) trains generally can't be used with (unpacked, assembled) bikes.
For IC (inter city) and EC (euro city), a reservation in advance is needed.
Almost all other trains transport bikes without previous reservation. There are some exceptions in the suburban railway systems around some larger cities such as Hamburg or in the Rhein/Ruhr area, where bikes are not transported during the morning rush-hour.
As already posted, ICE (inter city express) trains generally can't be used with (unpacked, assembled) bikes.
For IC (inter city) and EC (euro city), a reservation in advance is needed.
Almost all other trains transport bikes without previous reservation. There are some exceptions in the suburban railway systems around some larger cities such as Hamburg or in the Rhein/Ruhr area, where bikes are not transported during the morning rush-hour.
The German Rail website http://reiseauskunft.bahn.de/ provides a lookup function for bike-compatible connections.