Rabbits love to munch on everything from broccoli and beans to pansies and petunias. Even bushes and trees such as forsythia and flowering crabapple are fair game to these fluffy-tailed herbivores.

Sulp and Martin Enn run Happy Hops (Rõõmsad Hüpped), Estonia's only rabbit rescue, out of their own home. "Starting up this shelter just sort of snowballed somehow," Sulp recalled. "Our first two ...