Yes, Bitcoin can be traced. Bitcoin is actually built on the basis of blockchain, a public ledger. This means by default everyone will be able to lookup a Bitcoin address and figure out the entire transaction history of the Bitcoin. Every transaction is forever recorded on the Blockchain. Although a single person could have multiple bitcoin addresses and the addresses are not necessarily tied to a single identity, as soon as an address is linked to an individual, the trail of transactions associated with the individual could be followed to potentially uncover a significant part of his/her purchasing activity. You can lookup the transaction records of any bitcoin address via this site ( https://bitref.com ). If you are looking for cryptocurrencies that is untraceable, Monero is one of the popular options. We are going to cover more on anonymous cryptocurrencies in the near future. Will drop you a link when we finally do. Hope that this clears your doubt.
CryptoKnight Edited answer