One eye is more red than the other, what could be the cause?

Could be pinkeye: If this is something new, it could be pinkeye. Pink eye is often caused by a virus and often no treatment is needed (execept few cases such as cause by herpes/chicken pox viruses). Bacterial conjunctivitis usually causes significant purulent discharges, matting of the lids, and sticky eye lashes etc...And requires antibiotic drops etc.. If you have pain or change in vision, see you doc asap.

Multiple: If this is of recent onset, it is likely to be either bleeding, infection, trauma or internal inflammation. Most eye conditions affect one eye first and sometimes only one eye. If the vision is diminishing, or there is pain, light sensitivity or pus, then you should see an ophthalmologist to sort it out and start treatment.