I am using the same password for some encrypted files currently (I know this is bad practice, though), and I wonder whether an attacker could decrypt if one decrypted file fell into his hands.
Any good software should use PBKDF (a password based key derivation function) that uses a random salt. This salt is stored with the ciphertext and should be different for each ciphertext. As long as this is the case they key will be different for each ciphertext.
The best way an attacker can then attack your ciphertext (when stored on disk) is to iterate over the most likely passwords and perform the PBKDF. So the password and PBKDF together will provide the barrier that the attacker has to take. That is, if there are no other vulnerabilities to the crypto system, this is about the general case.
If you don't want to type a (different) password for each encrypt and if you want to use the same password each time, you might be better off using PGP encryption/decryption with a public / private key pair. PGP directly uses a public key for encryption and will request the same password each time to decrypt the private key, which decrypts the session key, which decrypts the data.
It really depends on you block cipher mode of operation and likeliness between your files. With any proper implementation, it should really not, but since you don't really give any details about your encryption scheme, it's hard to tell.
(side-note: how do you derive the key from the password?)