With careful, slow introductions, rabbits and other species can become lifelong friends.
A really good book I like on the subject is Living With A House Rabbit by Linda Dyke and Helen Flack. It has chapters on introducing cats and dogs to your rabbit, as well as great potty training/house training tips and advice.
RABBIT/DOG: Dogs are one of rabbit's natural enemies. Needless to say, if your dog goes chasing after squirrels and attacks birds, chances are it'll try to do the same thing to your rabbit. A puppy or young dog can just play to roughly with the rabbit and unintentionally kill it. The dog and rabbit don't necessarily have to be bonds - what you are aiming for is that they will at least not care about each other and leave each other alone.
RABBIT/CAT: Rabbits and cats can be good friends, as they have very similar body language. However, a cat that brings small rodents to your doorstep may be tempted to do the same to your new pet.
With introducing both of these pets to your rabbit, always take your time and make sure to NOT force the bunny and resident pet to be friends. Do NOT under any circumstances, leave the rabbit and other pet (cat or dog), alone together. Without you there to enforce safety for the rabbit's sake, bad things can happen. Make sure you also give the same amount of attention and love to each pet, as one can become jealous and act out.
One of my new bunny owners had a resident dog and two cats before they bought their rabbit from me. They have 4 "phases" that take the bonding of the animals slow and steady. Phase number 1 is smelling each other, but not having any access to each other. Phase 2 is being able to see and smell each other (one of their cats seems pretty interested in Effie below). Phase 2 is in process for several weeks before Phase 3, which is having the rabbit out of cage, with the cats and dog, seeing, smelling and touching each other, supervision during the whole procedure. I think everyone should introduce their rabbit to their resident pets this way.