As it stands right now, the only way to get experience is from killing monsters. This makes killing monsters too important in a game with such basic combat mechanics, and where people can so easily set up monster funneling machines. It's been said that experience was meant to be a motivation to get out of your home and kill some monsters, but I think that's a bad idea. What we *should* be motivating the player to do is to get out of their homes and explore the environment, and experience can be another reward for doing so.
Here's what I'm suggesting: Experience Scrolls. They are one-time use items, using them grants you a large amount of XP. They can be found in chests all over the world, in dungeons, mine-shafts, and strongholds. Maybe even in natural forming caves, although it might be a bit weird to find random chests in those.
As it is now, there's not a whole lot of reason to spelunk in caves above the diamond level, and there's not much reason to explore mineshafts once you've found melon/pumpkin seeds. This would give the player a very nice incentive to explore those things, which would add a lot of fun to the game.
I would also like to see other ways of acquiring experience, such as trading with villagers. Perhaps villagers will trade experience scrolls for certain amounts of material. It would give villagers a much needed purpose.
The nice thing about both these ideas is that they promote an adventure style gameplay that is fun. In the current build of the game, the only way to get high levels of XP is to grind for hours, which is NOT fun. It would be great if there was finally a real reason to explore other than just spreading light everywhere.