As others have mentioned before, avoid grapes and raisins since they are definitely toxic. Avocado seems to be mixed. The ASPCA maintains that the avocado is toxic to animals like horses and rabbits, but admits that there is little evidence outside one incident of avocado being toxic to dogs. Still it advises to avoid feeding avocado to dogs just to be safe.
ASPCA - Virtual Pet Behaviorist - Foods That Are Hazardous to Dogs
However, there are a lot of people who swear by avocado for their dogs, and there is even an avocado based dog food on the market (Avoderm). Personally, I never had a problem giving my dog an occasional bite or two, but do whatever you feel comfortable with. A smaller dog might not tolerate it so well. If you do decide to give your dog avocado, give a small sample and keep a watchful eye for any adverse reactions. If your dog seems even the least bit affected by it, stop feeding avocado immediately.
As for good fruits for dogs, there are a lot to choose from: apples and peaches (again, as someone mentioned earlier, avoid seeds since they contain cyanide), bananas, melons, a lot of berries. My own dog doesn't particularly like most fruits, but after a bit of experimenting I found that she loves blueberries and mango.
Be aware that while fruits are fairly healthy snacks, they are still high in sugar and fiber. Feed sparingly or not at all if your dog is diabetic. Fruits in moderation are okay for healthier dogs, but again too much sugar can lead to weight gain if your dog isn't active enough. Even if your dog is an athlete, all the fiber in all those fruits and veggies can lead to bigger loads and more frequent bathroom breaks if they eat too much. Though that last bit is more of an inconvenience than an actual health concern.