They are no danger if you kill them early enough. Pistols will suffice. If they are attacking your head, jump back or make a roll, to get a bit of distance between you and them. You will meet bats in the first two sections of the game.
Wolves are nasty beast, if they come to close and you get caught in a corner. Keep enough distance and while fighting roll and jump in all directions if necessary. Keep shooting all the while. Most of the time wolves will appear in packs of two or three. You will meet them everywhere in Peru.
If the bear can reach you, use the shotgun. He is very dangerous. Try shooting him from somewhere above if possible. In that case pistols will suffice. You will meet bears in "The Cave" and "City of Vilcabamba".
Velociraptor (The Lost Valley):
The Velociraptor is very dangerous. Here you should pick a good weapon. In the area where you meet the raptors first you can find the shotgun. This might prove helpful, but you will also need it against another opponent. Try to shoot raptors from above, while standing on a rock, or keep moving. Try not to get caught in a corner. You will meet raptors in "The Lost Valley" and "Tomb of Qualopec".
T-Rex (The Lost Valley):
In the area where you meet the raptors for the first time you will also encounter the T-Rex. He is very mean and will try to bite Lara's head off. So stay away from his head. Jump backwards early enough to stay out of it's reach. Keep shooting at him the whole time. It might become necessary to change direction, or you might be pressed against the wall. You can also try to stand in a cave entrance and shoot the T-Rex from there, where he cannot reach you. There is only one T-Rex in Tomb Raider I.
Larson (Tomb of Qualopec):
In the last level of the Peru part "Tomb of Qualopec" Lara will find out, that Larson is after her. He'll shoot at here, when she's in the pool or climbs out. Shoot back while circling him, till he drops to the ground. Larson will reappear in Egypt later on. There you have to chase him away by shooting at him. In the Sanctuary of the Scion you have to kill him to get the last part of the Scion.
Lions (St. Francis' Folly):
Lions are similar to Wolves. Advance carefully and you won't have to deal with more than one lion at once. In some areas you will find rocks you can climb onto to shoot the lions from above. In this case use pistols. Otherwise, keep some distance and jump backwards while shooting at them. You will meet lions in the whole St. Francis section.
Gorillas (St. Francis' Folly):
In the St. Francis part you will also meet gorillas. They will attack Lara and start hitting at her. Again keep your distance and keep shooting. Keep hopping back while shooting and the Pistols will suffice.
Pierre (St. Francis' Folly):
Pierre is Larson's colleague and as annoying. Whenever he appears you have to shoot back at him to chase him away. Don't run after him, since he would stay longer. If you can flee instead of returning fire, do so. You won't be able to kill him till the Tomb of Tihocan. He will appear in the whole St. Francis section.
Crocodiles (St. Francis' Folly):
Most of the time you will encounter them in a pool. As you have no harpoon gun you have to climb out and kill them from there. Before jumping into any pools have a look out for crocodiles. One hit with the shotgun might suffice. However if they are in the water kill them with the guns to preserve ammo. If you meet them outside of the water try climbing on rocks, or keep jumping backwards, while shooting at them. You will meet crocodiles in the "St. Francis" part and in "Egypt".
Giant Rats (Palace of Midas):
Most of the time the rats will be harmless, since they cannot reach you. Always look down before jumping and if there are any rats in the area kill them first. They can be found in the water or nearby, outside of the water. A few shots with the pistols suffice. You'll encounter rats in the Palace of Midas and the Cistern.
Centaurs (Tomb of Tihocan):
From the Tomb of Tihocan Level on, you will encounter the Centaurs. At first you will meet them as statues that come to life. Keep some distance and jump sideways while shooting at them. Hide behind walls or rocks if possible.