Can a cavity spread to another adjacent tooth?

Yes: Dentists commonly find what some call "kissing lesions" on x rays between the teeth where decay from one tooth affects the neighbor. Also in general terms dental decay is an infection and the more untreated cavities there are in a persons mouth the higher the risk becomes for the uninfected teeth.

Yes: If its an interproximal cavity it can involve the approximating tooth. Hope this helps.

Not really but...: However, what causes tooth decay can affect adjacent teeth at the same time. Further, when one has an existing cavity interproximally (between the teeth), there is a greater chance of decay forming on the adjacent tooth since as the tooth enamel is destroyed, more food and bacteria accumulate in that area, and the acid that is produced will affect the enamel on the adjacent tooth as well.

Of course: via our saliva, it spreads to adjacent and opposite teeth. You should get to the dentist ASAP to stop this process before it gets too bad. Take care.