We have had a blockbuster question, asking about the complexity of the cockpit, which was answered very well. With so many controls, are there any flight- or safety-critical functions which cannot be controlled by the cockpit?
You cannot (as far as I know),
- Flush the toilets
- Control the IFE system (aside from possibly pulling the breaker to shut it off)(there seems to be some debate on this one and it could vary by plane/system)
- Open the doors (of a passenger plane, cargo planes this may be possible)
- Update the software for glass cockpit planes (if the computers are not located in the cockpit). I'm still looking for the link but FMS units are updated via USB on a unit usually housed with the other flight computers which is often below the cockpit. In some smaller planes these units are in the cockpit as are the USB ports so this may only hold for some aircraft.
- General passenger tasks (reading lights etc). Although it should be noted that generally speaking the master breakers are in the cockpit so while they may not have control over individual system components (e.g. single reading lights) they can often shut them down completely if need be.
- Ovens (for heating meals) and coffee machines. Only circuit breakers are in cockpit again (and they are needed; faults in these things cause relatively high fraction of diversions).
In addition to many other things listed in answers, the biggest thing that pilots can't control from cockpit are "tools" like drunk passengers, cell-phone during flight users, loud passenger groups. And excluded from "tools" category, but still uncontrollable are babies. :)