I must say I've also had a connection with animals since I know myself... Anyway, my communication is usually silent, as in sittin staring/petting/etc for hours, but I feel what an animal wants from me. I am also quite stubborn, so I have conflicts, especially with my cat (I think it's a territorial thing, I'm quite territorial myself and he doesn't like it very much XD), but I know whom to approach and whom to avoid for that matter. I see animals as normal beings that have the same rights as I do, and I treat them accordingly. I usually have the strongest connections with cats, dogs, guinea pigs, parrots (any kind), birds of any kind (especially chicken - they love sleeping to my singing, what else to say..
) ), horses and ironically spiders (I'm not a fan of bugs, but I've had my share of saved spiders from deadly situations). The strongest feedback I had was from budgies. They love compliments and - girls especially - could listen for hours to stuff like : "you're so beautiful, look at your feathers, your colours, etc.". My last generation of budgies had a bell on their cage and they would get out and ring the bell if they wanted attention... and that was OFTEN!! I usually talk to pidgeons and sparrows too. Had quite a meeting with a hawk: we stared at each other for about half an hour and it gave me the strength I needed.
Oh, and about cats, it's said that they sit on your lap to draw all your negative energy and then they take it out ouside... I really got to believe that, my Jazzy did that especially with my dad, they have a very strong bond (I got my gift from my dad, he's also very comunicative with animals).