If you use AES Cipher Block Chaining (CBC) mode, you're generally good, as the IV + XORing of the previous blocks + the avalanche effect ensures that even encrypting all 0 has random-looking ciphertext.
Do I understand correctly, that with AES and other block ciphers if the plaintext has repeating 16-byte-aligned-and-long regions, they will correspond to repeating ciphertext regions?