Yes and no. In the 1.8.1 patch, Notch released an experience system, and when you kill monsters they will drop some orbs. When you collect these orbs, a little bar under your food and health bar will rise. When it gets to the top, it will start over again. However, you don't really level up, and you don't get any more strength or better armor or anything. But this is probably something that Notch is working on, and hopefully it will be released in the next patch.
EDIT: It is now confirmed that the ability to spend Skill Points will be added in the 1.9 patch.
There are levels, yes. Killing mobs, mining ores and smelting will give you experience. The only thing experience does is let you enchant items, they all have an experience level cost which is deducted from your total.
You will get slightly better armour and slightly better damage
You "spend" the levels on a enchanting table to get better tools and weapons
You put bookshelves around it.
Surround the table with bookshelves.
9
30
25
the more bookshelves you have, the higher the enchantment, and the more levels you enchant it with, the better it will be.
With the normal Minecraft mechanics, experience levels are only related to enchanting. You can mine cobblestone, or any other material, at any level.
Level 30, although you can have more than 30 levels.
As of the latest update, you do not need XP levels to be able to enchant in creative. That's because you can't gain levels in creative anyway.
You probably don't have enough experience levels for whatever you're trying to enchant. Each enchantment has a cost, if it says 12, it costs 12 levels.
In terms of what your asking, I am speaking from a neutral side here, but Minecraft is with online regristrations, but Mario clearly shoots Minecraft out of the water with the legacy, kid friendly and easy gameplay, though you must remember, you can continue to argue due to the fact one is oriented around building, mining, fighting zombies and such, while the other has an Italian plumber jumping from levels to levels.
Only when you are on easy, normal, hard. They also only spawn in light levels under 7.