Yes, but I believe 3DES has an effective key length of only 112 bits. Of course, even this is more than sufficient for a long time to come. 3DES can have an effective key length of 168 bits if 3 keys are used instead of two. There are no security problems that I know of from using 3 keys.
The Meet In The Middle attack (MITM, not to be confused with Man In The Middle) is a time-memory tradeoff that works against any multiple encryption. Triple encryption: ciphertext = encrypt(k3, decrypt(k2, encrypt(k1, plaintext))) plaintext = decrypt(k3, encrypt(k2, decrypt(k1, ciphertext))) An MITM attack, as I understand it, works by decrypting from one end and encrypting from the other... Step 1- decrypt(x3, ciphertext) for every possible x3, and store all the results. This requires 2^56 operations and 2^56*8 bytes (550 petabytes?) of memory when done against 3DES. Quite a lot, but it might be doable. Step 2- decrypt(x2, encrypt(x1, plaintext)) for every possible x1,x2. This require 2^112 steps with 3DES. If the result you get can be found in the table built by step 1 then you've figured all three keys.