It is not known yet whether or not mobile phones are harmful. Perhaps in ten or twenty years time if all the heavy users of mobile phones get brain cancer we will know. Cordless phones transmit lower energies than mobiles so are less likely to be harmful, but it is still the case that no-one knows if they are safe. Personally, I prefer to not take the risk as I don't find it that inconvenient to use a corded phone.
From the fact that cordless phones have a shorter range (measured in metres) compared with that of mobiles (more like kilometres) you can deduce that the output of portables has much lower energy. Additionally, cordless phones operate on different frequencies from mobiles (not unlike a number of other wireless gadgets in the home - FM). While there are no universally accepted accepted research findings, there is nothing like the same concern over cordeless phones as with mobiles. There is one school of thought which states that ALL electromagnetic "pollution" is harmful. This too is not proven to general acceptance levels.
Wow, that is the second time recently that someone has been posting an answer at precisely the same time as I - it was not my intention to seem to repeat what someone else has said, but it is nice to know someone agrees with me.