The short answer is yes, it's possible.
The longer answer depends on how long you want to run them for (and if you want the car battery to be able to start a car afterwards )
If your planning on buying a 12V battery specially to do this then I'd recommend ( as others have sugested ) getting a deep cycle ( or lesiure battery ) or a Sealed Lead Acid ( often abrebviated SLA ) battery for it. They are much happier at lower states of charge than car batteries so you will actually probably end up spending more on car batteries in the mid to long term than it would cost to get a dedicated lesiure battery. The jump star charger units that have been suggested generally contain SLAs and a cigarette lighter socket, which makes them quite usefull as they can be charged up from the lighter socket in the car. Car batteries are designed to give a high short term output for starting a car not to be run continuiosly.
If you've not already got the stereo you might want to consider buying a car stereo as that's already 12V and voltage transformations you make will involve losses of power ( read running time ) and can be wired straight to the battery.
You might like to use different speakers to car stereo ones. Depends on how much value you put on the quality of sound really, but most (medium quality ) in car speakers aren't that bad nowadays. That car speakers tend to be a lower resistance that home hifi ones ( 4 ohms as opossed to 8 ohm ) means they tend to be louder for the same input, which will increase the run time of the system as a whole if kept at a similar volume. Also worth noting is the quieter you run it the longer it'll last.
Running a laptop, as already sugested might be best to get a lighter socket adapter from the maunfactures as laptops tend to be worth a bit more money than a cheap stereo. Run times- laptops ( apologies for the little bit of maths ) seem to run at around 30-40Watts that's around 3Amps from a 12V battery so from a say 60 Amp battery expect a bit less than 20 hours run time with a lesiure battery a bit less than that from a SLA and significantly less from a car battery
As small car stereo will probably use about the same, halve those times if using both at the same time, a large stereo will use a lot more and may only run for a couple of hours. As a comparison 2 car headlight ( at around 45Watts each ) left on will flatten a car battery in a matter of a few hours.
Solar panels. Small ones can be just wired direct onto the battery but unless they have a blocking diode ( which will only cost a couple of £s at most ) should be unwired again when they're not in sunshine, as without the diode they will actually take power from the battery during those times.
If your thinking of the little batterty top up panels ( around £10-20 ) they are only about 1-2Watts each and are hardly going to make a difference to you charge when your using such amounts of power as you will for a laptop/stereo. If it's free it worth it if not don't bother buying one
A 5Watt pannel in constant sunshine for 10 hours will charge enough to run your laptop for little over an hour
For anything over a couple of watts ( ie anything usefull, say 15-55Watts ) I'd recommend sticking one of these in the circuit
http://www.maplin.co.uk/Search.aspx...rue&Stock=28&MinPrice=0&MaxPrice=9999&SD=true
Very easy to do, just connect the panel + and - to the wires labled solar cell + and -. similarly with the battery, accumulator is just another word for battery in this case.
15-20Watts of solar panel is gong to cost around £100 in case your thinking of going that route and unlees you keep moving them so they're in direct sunshine going to only give that out for about 2 hours of the ( sunny ) day, about a third or quater that during overcast times. If your do use them moving them every 2-3 hours so they directly face the sun make a large difference to the daily battery charge as can aranging aluminium foil to reflect light onto them ( you'll still only get the rated power but get it for longer )
