As of 1.1 bows can be enchanted, what enchantments can they be given and what approximate level are they?
- Power - Extra damage (Up to Level 5)
- Punch - Knockback effect (Up to Level 2)
- Infinity - As long as there is one arrow in your inventory, you will have infinite arrows.
- Flame - Sets arrows and mobs on fire.
- Unbreaking - Extra Durability (Up to Level 3)
- Mending - Increases the item's durability as you gain XP (only costs XP to enchant initially)
Taken from the Minecraft Wiki.
Enchanting infinity on a bow will make your bow behave similar to a creative bow. Even if you only have even 1 arrow in your inventory you'll have the ability to shoot as many arrows as you want. If you get a high level enchantment, you may also get a flame or punch enchantment as well.