Animals in MM serve a variety of purposes, most importantly that of food sources. However some animals (like Lions) are aggressive and will not take kindly to you encroaching on their territory, so watch out!
Here is a list of the animals in S2 MM, split into Aggressive and Passive. (Don't get rid of the large spaces when editting this page, please. :) )
These are fast, agile predators. They are much quicker than your player and attack extremely fast. (I am unfamliar with this animal, my only experience being during vanilla game play. Someone with more experience, please add to this!)
These are the only flying aggressive animals, and are extremely dangerous. They are quick, agile, and very hard to hit. But they will have no trouble hitting you. Approach with extreme caution. (This is another animal I am unfamiliar with, my only encounter with them being on the mountain in the Free Stranded map, after which I almost immediatly was killed. However, I believe they guard the lava forge. I am not certain however. Please someone clear this up for me.)
20 Oil, 10 Tooth, 4 Raw Shark Meat, 2 Fat, and 1 Shark Fin
A land shark is only encountered if the difficulty is listed as "Hard". If you attack a shark while out of water, the shark will fly out of the water to attack you. This will be accompanied with a bright red banner reading "LANDSHARK: ENABLED. FIGHT ME LIKE A MAN!". The landshark behaves like an eagle. In future versions, it will drop grenades while above the player and fire lasers that set fire.
2 Meat, 2 Raw Steak, 6 Fat, 4 Tooth, 4 Claw, 2 Skin, and 1 Liver
The lion is probably the first aggressive animal you will encounter, being the only aggressive animal on the first island in adventure mode. Be careful when going to their side of the island to collect clay and bamboo, Lions are almost twice as quick as your player, and their attacks, while also causing large amounts of damage, can inflict Bleed and Broken Bones on your character so keep Blueblossom and splints handy when fighting them. If they catch you unprepared, your best bet is to run towards the ocean and swim away, lions cannot swim and will lose interest in you once you swim far enough from shore.
This small, slow moving predator is not to be taken lightly and should be killed on sight due to its disturbing tendancy to wander into campsites. While it does little damage it can, and will, poison your character if it manages to land a hit. The posionous goop it drops can be used to make poison, which in turn can be used to poison weapons and it is the only animal in the game that drops this.
These animals slowly soar across the sky and never land, so you will need a ranged weapon to get them. Still, their slow movement and turn speed make them pretty easy targets even if you are only armed with a short bow.
In the vanilla game, catching butterflies increases you weight capacity (due to butterflies being -500 grams in weight), however in MM they weigh 1 gram, meaning that they are useless besides killing them and looting their corpses for insect parts.
This plentiful, slow moving animal is a perfect source of food when just starting out. They wander around on the shoreline of the islands. If attacked they will run away, but do so so slowly that it isn't an issue. The ease of killing them is offset by their small drops, but they are still a useful resource when you are unable to take on bigger and better game.
4 Small Meat, 2 Tooth, 2 Fat, 1 Liver, and 1 Skin.
This quick, agile animal is a good, risk free, source of skins. They are quicker than the player by a fair margin, and it can be hard to hit them with ranged attacks due to their tendancy to make sudden, quick turns. However, this random pathing also causes them to get stuck behind a tree or rocks at fairly regular intervals, leaving them open to being attacked without fear of missing. They can be tamed by putting at least 5 bananas in your hand and throwing at them. Once tamed you can order them to get water, branches, leaves, stones and food.
Parrots are another fast, agile animal, with quick turning speeds. Unlike the Bird, however, Parrots do land, and while they will take off if you get too close, you are more than welcome to range them while they sit on the ground.