In reply to Elguera:
Top 4 criteria:
1. Fast-drying, as they WILL get wet and you don't want them to stay that way any longer than necessary
2. Durable fabric, because you WILL walk into sharp sticks/trees/roots hidden in the undergrowth - boots rather than shoes will be better for this and also better for preventing ants and other crawlies from getting in (tucking trousers into socks helps, and use gaiters if the insect-life gets really bad)
3. Firm sole, because otherwise your feet will get tired from walking for hours on an uneven bed of tree roots
4. Light weight, as you tend to be constantly stepping over things and I'd think that would get very tiring if you had heavy boots on. Heavy also tends to mean slow-drying.
If it isn't wet season or you aren't going to be in thick forest for long then you can get away with wearing pretty much any shoes or boots (including trainers), so take whatever you feel comfortable wearing; but the longer, denser and wetter it gets the more you'll be thankful for the protection your footwear gives rather than how comfortable it feels on your feet.