From recent researches, I get the impression that some of the higher up the range Siemens ones can do more than just block specific numbers, but you'd have to look them up and read the instruction manuals online (something I tend to do whenever making a significant purchase).
We've got Panasonic ones, which can only block specific numbers, and whilst they work OK, the display really is rather tacky looking. Somewhere I'm convinced I've seen an Android DECT phone, but damned if I know where! Why does no-one seem to make a base station with a wired phone (so it keeps working in a power cut) but with DECT satellites?
Sadly, of course the Telephone Preference service can't help with the ubiquitous overseas ("out of area" is all our phone says) presumably marketing messages. I never know what they say, as our answering machine is always on, and we just ignore them, as they never respond to the answering machine.