Is it possible to scuba dive and keep your ears dry?

Hmm… There’s always a “dry suit” but it’s a tad pricey. Plugs are dangerous because the pressure can rupture your tympanic membrane, which always ruins all the fun. Be creative, and look around though, but expect whatever you put around your ears to get a little tight as you dive down.

Not really. As @Smashley mentioned, a dry suit would keep them dry, but they are very expensive, and typically used in extreme arctic temperatures. Aside from that, there really isn’t much that would keep your ears dry. They can’t be plugged, because they need to be used as a pressure release as you equalize with depth.

I’m not sure there is anyway to prevent water from getting into your ears while diving with the exception of a well fitted drysuit. From what I’ve heard the drysuit hoods can be difficult and will still get water in them if you don’t have a really good fit/seal. If the only thing your worried about are ear infections you should take a look at these ear drops, or any other kind. Some of them use alcohol to kill all the bacteria that gets in your ears. I always just use a couple of drops of rubbing alcohol in mine. I’ve also heard you can use a 1:1 mixture of vinegar and alcohol (never tried it, smells like crap).

Another option is the Sahara Ear Dryer. It was developed by an ENT physician to have safe temperatures, air pressure and sound pressure levels. It feels really good and can be used for ore than one drying cycle if needed.
(BTW, I’m an Audiologist)