Does Android put wifi and other data networks to sleep when the display is turned off?
It depends, some Android devices have an advanced setting WiFi Sleep Policy under

Settings -&gt; Wireless -&gt; Wi-Fi Settings -&gt; [Menu Button] Advanced -&gt; Wi-Fi Sleep Policy

But I am not sure if this is a vanilla Android feature or an manufacturer modification. At least the Galaxy S series has this setting.

Data networks are usually fully active. But Apps like Tasker allow you to define certain profiles to improve battery life. For example: Only allow 2G when the display is off, because 2G requires less battery then 3G (UMTS).