Transactions normally include a small fee, to incentivize miners and disincentivize abuse. You don't have to pay the fee, but if there are more transactions being broadcast than the blockchain can accommodate, the fee-paying ones get priority. (It's a little more complicated than that: when you generate a transaction, you choose whatever fee you want, and they get prioritized based on a combination of the fee, the transaction size in KB, and how long it's been since those coins were last moved.)

Current transaction fees are typically in the range of 0.1-0.5mBTC, so in order to continuously flood out everyone else, you'd need to spend more than 2.5BTC/hour in fees.