Is it possible to have damage bonus without any requirements?

Usually it is like 15% more dmg while above 50% hp or something like that but how about mere 15% more dmg which keeps the bonus all the time?

Doubtful. If you ever found such a weapon, it would be the most valuable in the game.

Does this fit your description?

That axe has a requirement for the +14% of energy regeneration -1.

I cannot imagine that anyone would prefer that ofer a "while in Stance," "while health is above 50%," "while enchanted," or any such mod.

If you can afford a -1 to you r energy regen, you need to get your hands on a zealous haft, hilt, or string.

Just my $.03

Supposedly in the olden days of GW, those items exists, but no longer. They all have requirements now. If you ever do run across one now a days, please let me know ... keep hope alive!

I've got a composite bow that has no requirement for it's +13%. It does have the negative of -10 armor while attacking though.

I've seen those as well. I consider those requirements, because you have to have that negative effect along with the damage bonus. I guess "requirement" is not the right word ... I should say "restrictions".

So do mobs still drop items that has a damage bonus and no restrictions?

Customization? :P
I don't think there's really any damage bonus without requirements except customization, really. None that I can think of, anyway.