A 128-bit key for AES need only be 128 bits long. No other properties are required, though other properties might be desired.
If you choose a 16-character string, then you're not really using those 128 bits to their fullest. ASCII only supports 7 bits per character (the first bit of each byte is always zero), and your real-world entropy top out at around 6 bits per character of ASCII text. So a 16-character password if used directly for 128-bit AES has the same level of security as a 96-bit key, rather than 128-bit key.
For an encryption key, you want to use those precious bits to their fullest; you want each bit to be equally unguessable.
The best way to do that is to use a hash. The cool thing about using a hash is your password doesn't have to be exactly 16 characters; it can be shorter or it can be longer, and you will still get a consistently random distribution of bits in your resulting key.
MD5 will produce a 128-bit output, so that's convenient. But really, MD5 is pretty broken and your hash output doesn't need to be exactly the same size as your key, it just has to be at least as big as your key. You could just as well use SHA-256 and then just take the first 128 bits of hash output for your key. Or the last 128 bits. Or the middle 128 bits. As long as you're consistent, it doesn't matter.
Which, as long as it doesn't matter, how about we run the hash several times. That way an attacker will have to run the hash several times for each guess if he wants to guess our password.
Actually, someone's already thought of this, and there is a list of "Key Derivation Functions" specifically designed to take an arbitrary input of any type and size and produce a key at least X bits long, often with the added property that deriving the key from the password takes a LONG time (and perhaps a LOT of memory).
These have been discussed pretty extensively here, so just search for PBKDF2 or scrypt for more details.
So to summarize, the answer is yes it works, but no you shouldn't do it because there are better options ready-made that make your keys better in every way.