As Beers said this bit depends on how things are setup on the shared network.
If you are using an unsecured wireless connection anyone within range can capture your traffic of the network.
Further if the wireless network does not use wireless isolation then it could be easy for someone to get your traffic easier even using a secure wireless connection.
WEP is far less secure, and far easier to crack, than WPA but remember that any 'security' is only as secure as a fence around your house. If someone wants in they will get in.
As for a wired shared network you can still often capture packets of others on the network.
Always ensure that sites you visit using passwords use SSL. This will help secure your traffic from prying eyes.
Definitely ensure that you are not sharing folders on your computer when using unsecured wireless connections.
A paid VPN service, or if you already rent a VPS or dedicated you can setup a VPN, will further help secure your traffic on the wireless network if properly setup.