Spread Spectrum is very secure, no scanner can pick up the signal. Spread Spectrum does just what the name implies, it spreads the data bits over a pretty broad piece of the spectrum. The handset and base are constantly jumping to different frequencies in step with each other and, unless the scanner has the jump sequence, it will not be able to track the phone. A lot of the plain digital phones use encryption between the handset and base. The better ones change the key for each new conversation so even if you could decrypt one call, the next one will use a completely different key.
As cbbrown said, most of the cheaper 5.8 Ghz phones use either 2.4 Ghz or 900 Mhz in one direction. The side-tone you hear in your handset (your voice in the ear piece) is generated in the base and sent back to the handset so any scanner that can hear the base's transmit will be able to hear both side of the conversation.
Read the box when you buy a cordless phone. If the box doesn't say "Spread Spectrum", it isn't, If it doesn't say "Digital", it isn't. If it doesn't say "Encrypted" or "Encoded", it isn't.