Cyclic peroxides can be obtained by cycloaddition of singlet oxygen (generated by UV radiation) to dienes.  An important example is rubrene.  Six-membered cyclic peroxides are called endo peroxides.  The four-membered dioxetanes can be obtained by 2+2 cycloaddition of oxygen to alkenes. 
The hazards associated with storage of ethers in air is attributed to the formation of hydroperoxides via the direct albeit slow reaction of triplet oxygen with C-H bonds.