Use timedelta to switch between timezones. All you need is the offset in hours between timezones. Don't have to fiddle with boundaries for all 6 elements of a datetime object. timedelta handles leap years, leap centuries, etc., too, with ease. You must first  
from datetime import datetime, timedelta
Then if offset is the timezone delta in hours:   
timeout = timein + timedelta(hours = offset) 
where timein and timeout are datetime objects. e.g.   
timein + timedelta(hours = -8) 
converts from GMT to PST.
So, how to determine offset? Here is a simple function provided you only have a few possibilities for conversion without using datetime objects that are timezone "aware" which some other answers nicely do. A bit manual, but sometimes clarity is best.
def change_timezone(timein, timezone, timezone_out):
    '''
    changes timezone between predefined timezone offsets to GMT
    timein - datetime object
    timezone - 'PST', 'PDT', 'GMT' (can add more as needed)
    timezone_out - 'PST', 'PDT', 'GMT' (can add more as needed)
    ''' 
    # simple table lookup        
    tz_offset =  {'PST': {'GMT': 8, 'PDT': 1, 'PST': 0}, \
                  'GMT': {'PST': -8, 'PDT': -7, 'GMT': 0}, \
                  'PDT': {'GMT': 7, 'PST': -1, 'PDT': 0}}
    try:
        offset = tz_offset[timezone][timezone_out]
    except:
        msg = 'Input timezone=' + timezone + ' OR output time zone=' + \
            timezone_out + ' not recognized'
        raise DateTimeError(msg)
    return timein + timedelta(hours = offset)
After looking at the numerous answers and playing around with the tightest code I can think of (for now) it seems best that all applications, where time is important and mixed timezones must be accounted for, should make a real effort to make all datetime objects "aware". Then it would seem the simplest answer is:
timeout = timein.astimezone(pytz.timezone("GMT"))
to convert to GMT for example. Of course, to convert to/from any other timezone you wish, local or otherwise, just use the appropriate timezone string that pytz understands (from pytz.all_timezones). Daylight savings time is then also taken into account.