I think it would be cool if there were some mobs that actually dug through the ground and avoided the surface/sunlight/lit areas. Some might be hostile, some might be neutral and only attack under certain conditions (like polar bears), others might just be completely passive:
1)Oozer (passive). They look a lot like a giant earthworm, but with large openings on either end (kind of like a long-sleeve shirt sleeve that's been removed from the shirt). They're a small mob, like silverfish or endermites, and so can be killed in one shot. However, you cannot actually kill them with tool swings as this will just spawn two new oozers; instead, you must kill them in water (must be three deep)/lava (2 deep) or isolate them from adjacent blocks. Oozers will avoid travelling through blocks exposed to air or liquids, and they won't move through obsidian. Blocks that oozers are travelling into will have a block-breaking animation to them, and they will turn into dirt once broken. You will not see an oozer in the open unless you break the block they happen to be in. When an oozer enters a block immediately beneath any plant that can still grow, it will have a 50% chance to apply a bonemeal effect (this is a one-time bonus applied during the move into the block, not an on-going one while it remains there).
2)land shark (hostile). Land sharks are the size of a prone creeper, they have a dirty grey coloration and feature a large horn on their head that helps them drill through the earth. As they move they replace the blocks they vacate with the blocks they're digging away, shifting the earth to make room for themselves. They can support sand and gravel if they drill under it, but because of the unstable nature of those materials they will periodically shake in a manner similar to a falling-sand entity bouncing on a fence. They have slightly more health and slightly more strength than the average zombie or skeleton, but otherwise have no special fighting abilities. They drop horns, which can be used as a crafting shortcut item for the ingredients involved in extended duration haste 2 potions (one landshark horn and one water bottle), but for reasons unknown this process doesn't always work and simply destroys both items (umm, I figure a 30% success rate is fair?).
3)Dowsers (neutral). Dowsers look like giant star-nosed moles and only generate in underground burrows. They come in three variations: brood mother (40 health, only spawns with burrow creation, model is a 2x2x2 mob displayed as laying on its side), bull (25 health, model is a 2x2x2 quadruped), and kit (10 health, model is a 1x2x1 quadruped). The burrow is originated with a nesting room, where the brood mother is laired. On burrow creation, she will spawn with a random combination of 20 kits and bulls and thereafter will spawn up to 20 kits to replenish the ranks. When she or her kits are attacked or otherwise taking damage, she sends out a pain call that teleports 25% of the bulls back to the nesting room to deal with the problem (they will block off leaks, break sand/gravel that is suffocating her, and attack intruders); she otherwise has no combat abilities. Kits grow up into bulls, but otherwise serve no purpose other than to randomly run around and occasionally take damage through normal AI quirkiness (thereby maintaining a bull presence in the nesting room). Bulls have a keen sense of ore detection (and a natural silk touch), and will tunnel through the ground to get to them. Upon harvesting the ore, they'll take it and the trash blocks back to the burrow to be deposited into the treasure rooms and trash rooms. Each type of block will have its own room dug out, at a size of 11x11x6. Blocks will be placed layer by layer in pyramid fashion with a 2-block space around the perimeter; upon a room becoming full a new room for that block type will be generated. For ore blocks, each block represents one block of ore; for trash blocks, each block represents a full stack. Bulls that encounter any player carrying ores will attack them, believing them to be thieves raiding the burrow. Bull dowsers drop a star nose that can be used to craft a dowsing rod (2 sticks with two star noses in the upper corners, forming a Y shape) that will lead the user to one vein of ore (it breaks when within 3 blocks of said vein, but otherwise provides no further info).
Mobs digging through the ground has the potential to wreck havoc on players. For example, what if you're in your house smelting some iron and all of a sudden a land shark jumps up through your floor and kills you? Or you've finally finished that scale replica of the Eiffel Tower, only for a swarm of Oozers to start eating it up?
The underground would be completely ruined with little one block tall tunnels everywhere. Imagine you're mining and you for the first time diamond ore- and then a Dowser shows up and swallows it whole!