I have to disagree with some of the advice being given... there's no need to reinvent the wheel here. Whatever stereo you choose should come with instructions as to what each wire should connect to; speakers, etc. The 'power' wires should be marked as 'switched' (i.e. turning on and off when the key is turned to the RUN position) and 'constant' (i.e. always hot).
The 'constant' power enables your stereo to conserve things like station settings (and in newer stereos, MP3 and album names, pictures etc.) You can easily find a constant power supply under the dash, and make a clean (and reversible) splice using commonly available connectors. Often, a cigarette lighter (if constant) is used.
The 'switched' power shuts down most components when the key is removed, avoiding draining your battery (for example, if the stereo has a hard time ejecting a CD and tries to do so over and over.) Again, your dash is probably filled with sources of switched power.
Unless you're running a massive stereo, amps and large speakers, the current draw should not be excessive. Even less so if replacing an existing stereo. As with any such work, take the opportunity to replace all your fuses, clean the fusebox contacts with emery paper and/or contact cleaner spray.
And if you really want to sit in the car, while turned off, and listen to the radio? Err... put the key in the ignition. Done and done.
My two cents,
Duncan, Ottawa
'78 Midget 1500
'77 VW Rabbit resto
'67 VV P1800 RIP