The XRP Ledger is a decentralized ledger, secured by cryptography and operated by a distributed peer-to-peer network of servers. This means that no one party, not even Ripple, can require a fee for access to the network.
However, the rules of the XRP Ledger include several types of fees, including neutral fees which protect the ledger against abuse. These neutral fees are not paid to anyone. There are also several optional ways that users can collect fees from each other, both inside and outside the XRP Ledger.
In the Ledger
The transaction cost (sometimes called the transaction fee) is a miniscule amount of XRP destroyed to send a transaction. This cost scales with the load of the network, which protects the peer-to-peer network from spam. See Transaction Cost for more information.
The reserve requirement is a minimum amount of XRP that an account must hold. It increases with the number of objects the account owns in the ledger. This disincentivizes users from increasing the size of the ledger carelessly or maliciously. See Reserves for more information.
Transfer fees are optional percentage fees that issuers can charge to transfer the currencies they issue to other addresses within the XRP Ledger. See Transfer Fees for more information.
Trust line quality is a setting that allows an account to value balances on a trust line at higher or lower than face value. This can lead to situations that are like charging a fee. Trust line quality does not apply to XRP, which is not tied to a trust line.
Outside the Ledger
Although the fees described above are the only fees built into the XRP Ledger, people can still invent ways to charge fees associated with the ledger. For example, financial institutions commonly charge their customers to send money into and out of the XRP Ledger.
Many other fees are also possible. Businesses might charge for access to a client application, maintenance of non-XRP Ledger accounts, exchange services (especially when buying XRP on a private market instead of within the XRP Ledger's decentralized exchange) and any number of other services. Always be aware of the fee schedule before doing business with any financial institution.