It depends on the chaining mode. AES is a block cipher, it is applied on blocks of 16 bytes (exactly). The chaining mode defines how input data becomes several such blocks, and how output blocks are then put together. Most chaining modes need to work with some sort of "start value", which is not secret but should change for every message: that is the IV.
Reusing the same IV is deadly if you use the CTR chaining mode. In CTR mode, AES is used on a sequence of successive counter values (beginning with the IV), and the resulting sequence of encrypted blocks is combined (by bitwise XOR) with the data to encrypt (or decrypt). If you use the same IV then you get the same sequence, which is the infamous "two-time pad". Basically, by XORing two encrypted string together, you get the XOR of the two cleartext data. This opens to an awful lot of attacks, and basically the whole thing is broken.
Things are less dire if you use CBC. In CBC, the data itself is broken into 16-byte blocks. When a block is to be encrypted, it is first XORed with the previous encrypted block. The IV has the role of the "-1" block (the previous encrypted block for the first block). The main consequence of reusing the IV is that if two messages begin with the same sequence of bytes then the encrypted messages will also be identical for a few blocks. This leaks data and opens the possibility of some attacks.
To sum up, do not do that. Using the same IV with the same key ever and ever defeats the whole purpose of the IV, the reason why a chaining mode with IV was used in the first place.