What can I do with all this Ebonstone?

You shouldn't use it as a building material because the presence of a lot of Ebonstone causes the sky and music transition seen in the Corruption, and allows Corrupted enemies to spawn.

What you could do with it:

• Place it in your inventory's trash slot to get rid of it; use Shift-Click for maximum efficiency.
• Place it, then purify it to get more Stone, if you happen to be short on that (which will never happen because half the map is Stone).
• Store it on the assumption that it does something useful at some point in the future.
• Use it to lock a passage to players who don't have a Nightmare Pickaxe or higher yet. Then again, other materials, such as Obsidian or Hellstone, would be better suited for such purposes.
• Use it to build a Corrupted enemy grinder for infinite Rotten Chunks.

As of patch 1.1, there are also a few more "real" uses:

• You can combine it with Demonite Ore to make Demonite Bricks, which are a feasible building material.
• After unlocking hardmode, the Corruption can spread via Stone Blocks as well, so you can get an Underground Corruption going by planting a few Ebonstone Blocks, then waiting for them to spread.