Hash function from narrower block cipher operated in CBC-encryption mode?
If the motivation is to rely on a DPA protected implementation of a block cipher, hash function constructions based on a block cipher (think of Davies-Meyer for instance with say Rijndael at 256-bit plaintext) could be used.
Alternatively, the issue of using small input size compression function to built secure hash functions with larger output size has been investigated in e.g. Nandi, INDOCRYPT 2005; Hirose, FSE 2006; Peyrin et al., Asiacrypt 2006 and following work, but is not entirely settled.

From an efficiency point of view, CBC-HASH is going to be at least $n$ times slower than any other hash function in the wild. (And practical security is always a balance between practicality, that is resources, and security.) In addition, the hash cannot be computed on the fly: one has to make $n$ passes over the message which is cumbersome in many scenarii (think embedded devices for instance).

Case $n=1$. Assuming the underlying block cipher is denoted by $E$, take whatever you want for the message blocks $M_i=N_i$, $l&gt;i&gt;1$ for some big $l$ and:


$M_0=0$ and $M_1=E_K(R)$,
$N_0=R$ and $N_1=E_K(0)$.


for some $R\neq 0$ if $IV=0$ and $R=IV$ otherwise.
Then, note that the hash output is the same, so that you have a collision for $M$ and $N$. This is possible because $K$ and $IV$ are known values.

Case $n=2$. Choose some index $\xi$ and choose the message blocks $M_1$, ..., $M_\xi$ and $N_1$, ..., $N_\xi$ randomly and choose the remaining message blocks so that $M_i=N_i$, $i=\xi+1, ..., l$. Then, use the trick above to ensure the key for the next round is identical for both messages (i.e. create a collision at stage $\xi$ during the first pass instead of at the beginning). Then, wait for a collision to happen in the 2-nd round at block $\xi$. It happens with probability 
${2^{block\_size/2}}$ for a primitive $E$ with block size $block\_size$. This appears to be possible as the first message blocks are randomly chosen.

Case $n&gt;2$. This procedure can be followed up to any round $n$ with complexity $2^{block\_size*{n-1\over2}}$.

Example. 
With the 3DES as $E$ and an hash output size of 512 bits, this leads to a collision attack for CBC-HASH with 8 rounds that has complexity $2^{32\cdot 7}$ instead of the $2^{32*8}$ of the birthday paradox. 

I am more generally concerned about the small "bandwidth" issue due to the use of an underlying CBC with a block cipher of small output size.