What would happen if someone spammed the network with millions of transactions?
Reminds me of a similar question I'm mesmerizing about:
Who sets the price of transactions? The network or the miners?
If it's the miner, could an entity set up a massive supercomputer, mine most blocks and then set the transaction fees to 99%?
The prices are not set, they are "decided" by the market composed of miners and people who need the miners to make their transactions. There is a limit of one MB of transaction data per block which has been arbitrarily decided for now. It may be increased or not in the future.
At least that is what I understood.
For the time being, if you go on blockexplorer.com, you will see that blocks don't often exceed 5KB. So there should be 995KB of transactions more still possible per 10 minutes. Hence, I have no idea why there are so many pending transactions. Maybe they are invalid?