What are some tactics to safely cross the Animated Forest in ADOM? I've got a level 9 troll barbarian with 44/26 DV/PV, and controlled teleportation but no way to teleport.
For a melee-focused non-caster, the easiest strategy is to set your defensive tactics to Coward and rest in place until you get a chance to move between the trees. It's very tedious and there's always the possibility that they'll gang up on you for no reason, but it's doable.
Go through the Dwarven Halls instead. Go far, go fast, and don't slow down for any monster!
(I realize this doesn't answer your question, but whenever I try walking through the Animated Forest, I end up fighting some trees. Either some fraction of them are hostile, or I'm clumsy; could be either. And once you start fighting trees, you can't stop, because fighting the hostile trees angers the non-hostile trees - and it's hard to tell which ones are hostile, from the up-to-eight trees surrounding you. Plus, trees spawn with time, so the level will eventually end up either impassable or violently logged.)
Equip two shields and just hold down in the direction you wish to go. The Dwarven Halls can generate some really scary monsters. The forest is much safer.
Alex's answer is a good one, but I'd like to expand slightly to explain why it works and what to do in some edge cases.
As Alex suggested, the safest way to pass the Animated Forest (by conventional means, anyways) is to equip two tower shields and set tactics to Coward. This works because, by equipping two shields, you will no longer auto-attack the neutral trees if you bump into them. Note that there is no confirmation of whether you actually want to attack when bumping into trees - you will just swing your sword. With two shields, however, this is disabled, as you cannot attack with a shield.
Coward mode grants extra defensive protection, to help you survive the rare hostile tree or other beastie that spawns. Fortunately, there will not be a lot of either of these, as the trees tend to squash anything hostile to them, which is most spawns.
As for movement: Patience. Wait in place until you have a move you can take. I suggest moving any time you have a chance to move in the general direction of the stairs you want, and AVOID THE WALLS if possible, as it is easy to get trapped there. You will occasionally find yourself trapped - cornered against a wall or simply surrounded in the open. Most of the time you can just wait a few turns and then move, but over time you will collect an entourage of hostile trees. If they get too numerous, you'll have to pull out a sword and kill a couple, otherwise you will find yourself completely trapped and unable to move as hostile trees will never move away from you. Just be careful - don't upset trees you don't need to.
Lastly, food is a major concern here, as it takes a long time to cross the forest, so bring extra.