I'm studying the Bitcoin system and I'm wondering if there's a way to anonymously buy Bitcoin. Is it possible to charge a wallet (e.g. with a credit card, PayPal account, by person, by snail mail, etc.), without being traceable? Let's suppose I don't trust any website/person...
The best way to do it is in person, with cash. Most other methods are traceable. Provided you don't live in the middle of nowhere, it's pretty easy to find at least someone nearby who's willing to buy, and if you're serious about anonymity that extra travel distance is probably a minor issue.
I agree with @nuggetbram, in person is the most practical way.
An alternative is buying from a BTC ATM, for cash. Those tend to charge very high fees, though, and would limit the amount you can buy per transaction (there should be no problem splitting to multiple transactions, though, as each is independently anonymous).
Due to strict anti money laundering (AML) regulations around the world, all major BTC exchanges (i.e. all the exchanges you can sort-of trust) employ Know Your Customer (KYC) controls, which make it impractical to use their services anonymously.
A bitcoin ATM. When it asks if you have a wallet, answer negatively to get a paper wallet printed for you. Then load the paper wallet and walk away. After that transaction is confirmed, sweep the paper wallet funds into your own personal wallet. As someone else noted, this is not the cheapest way to do things, but it is safer than meeting someone with cash.
Another option is to use cash to buy a pre-paid Visa (or MasterCard or American Express) card from a supermarket or convenience store. Then, create an account with an online exchange, and use the prepaid card to fund the account, then use the funds to buy bitcoins. To be sure to cover your tracks, use Tails/TOR when connecting to the online exchange.