From EUO Manual

LaughingCoyote's Animal Taming Guide

If you happen to have reasonably high defense (50+)and magic resistance (500)then getting the pet dragon that you want is pretty easy if you're willing to invest the time into it. The aim of the game is tame your way up to 100 taming using monsters that can't hurt you because of your defense or MR. This lets you semi-macro taming - just keep pressing f9 while you read the paper or something. Sometimes this means squeezing as much training as you can out of a monster - remember that you can train up to 15 lvls past the monster, it is just slower that way. I find it is also easier to semi-tame (grey) a bunch of monsters first, then go through them again so that you can use shift-f9 instead.

So here is a list of the monsters with the skill level required:

0-5 : Rabbits, cows and horses. Find them randomly around the continent map or in towns like Dryden or the Resort.
5-10: Rats, giant rats. Nord jail should have plenty, as well as the old mine.
10-15: Bats.
15-20: Gremlins. There's a whole bunch of them in a mine in Mountain Pass.
20-25: Goblins, orcs, goblin veterans.
25-30: Orc brutes, goblin elites.
30-35: Half orcs.
35-40: Fel orcs.
40-45: Trolls, Mongbats.
45-50: Hill giants, cyclops.
50-55: Ogres.
55-65: Snow ogres.
65-80: Minotaurs.
80-85: Ice ettins, imps.*
85-90: Crocodiles. Crocodiles found in and around Pride's Fall
90-95: Werewolves. Werewolves are hidden in Snowy Island.
95-100: Hydras.**
100: Drakes! 

*The only level where you can't avoid ranged monsters.

** For Fighters,Rogues and Mages, even with high MR, unless you are willing to use a lot of pots, it's probably better to stick with Werewolfs until you reach 100. For Mages who can Vas Mani, Hydras should be quicker.

Thanks to ChildProdigy, Gulnar and Aile for the tips.

Happy taming.