Generally speaking, most dogs like toys that simulate prey. This is why squeaky toys and soft toys are often very popular with most dogs. Hearing the high-pitched squeak and/or ripping apart a soft plush toy can be immensely satisfying to some dogs.
However, dogs are individuals, and even dogs within the same breed will have preferences due to personality differences. Some dogs prefer harder toys that feel good to chew on; others prefer toys like balls or Frisbees because they're fun to chase and retrieve; and some dogs don't like toys at all, unless their owner is in on the game.
Many people might think their dog has no interest in toys. It's best to introduce toy play when your dog is young. Younger dogs and puppies are naturally more playful than older dogs. For puppies, younger dogs, or even less confident older dogs, you can try soft plush toys or even toys with real fur attached. Some dogs just need something totally new and different to entice them to play!
Your dog’s toy preferences can change throughout his or her life. Many puppies prefer rubbery-type chew toys while they're teething, and senior dogs often like softer toys that are comfortable to hold and tug. During adulthood, your dog may need sturdier toys, such as thick ropes, or harder rubber balls.
If your dog likes to destroy soft toys, never let your dog have access when unsupervised. Ingesting a squeaker or a toy can cause very serious complications and may require surgery to remove what was ingested. Some toys should be "play with me" only; this means your dog can only have access to certain toys when he is playing tug or fetch with you. This applies especially to toys with real fur or to very soft plush toys. When the game is over, the toy should be stored out of your dog’s reach. This can increase the lifespan of the toy, too.
One other thing to keep in mind, in addition to what the toy is like, is how it is used. Humans are not very good at emulating their dogs’ play style. If your dog is very calm, and you suddenly start shoving a toy in her face to try to get her to play, then she’s not likely to be interested in that game. However, if you use a soft plush toy or a toy with real fur and tease her by dragging it on the ground and keeping it just out of reach, she may decide playing with you is tons of fun!
For these calmer dogs, make sure to let them "win" the game sometimes by releasing the toy when they pull on it. It can be discouraging to play tug and never win. If you need to get the toy back from your dog, simply trade her for a tasty treat, or better yet, have a second toy that's just as much fun as the first one and trade for the second toy. Try to end the game before your dog loses interest. Too much of a good thing can become boring, so keep your play sessions short and fun!