UPDATE: I recently learned from this question that in the entire discussion below, I (and I am sure others did too) was a bit confusing: What I keep calling a rainbow table, is in fact called a hash table. Rainbow tables are more complex creatures, and are actually a variant of Hellman Hash Chains. Though I believe the answer is still the same (since it doesn't come down to cryptanalysis), some of the discussion might be a bit skewed.
The question: "What are rainbow tables and how are they used?"
Typically, I always recommend using a cryptographically-strong random value as salt, to be used with hash functions (e.g. for passwords), such as to protect against Rainbow Table attacks.
But is it actually cryptographically necessary for the salt to be random? Would any unique value (unique per user, e.g. userId) suffice in this regard? It would in fact prevent using a single Rainbow Table to crack all (or most) passwords in the system...
But does lack of entropy really weaken the cryptographic strength of the hash functions?
Note, I am not asking about why to use salt, how to protect it (it doesn't need to be), using a single constant hash (don't), or what kind of hash function to use.
Just whether salt needs entropy or not.
Thanks all for the answers so far, but I'd like to focus on the areas I'm (a little) less familiar with. Mainly implications for cryptanalysis - I'd appreciate most if anyone has some input from the crypto-mathematical PoV.
Also, if there are additional vectors that hadn't been considered, that's great input too (see @Dave Sherohman point on multiple systems).
Beyond that, if you have any theory, idea or best practice - please back this up either with proof, attack scenario, or empirical evidence. Or even valid considerations for acceptable trade-offs... I'm fam