The best short answer is, "it depends."
Let's separate assets from down payment for a minute. Many other posts here on Trulia have addressed the down payment issue, so I'll assume you have this under control. Let me know if not.
Now that you have your loan structured, typically when it comes to assets, we are talking about reserves. Reserves are defined as:
A) Total assets divided by amount of housing payment (Principal, Interest, Taxes & Insurance). For example, if you have $20K in the bank and your housing payment is $2000/month, you have 10 months of reserves. OR....
B) Total assets divided by total debt service. So, further on the example above, let's say you have that same housing payment, but also a car payment of $500/month, now you have 8 months of reserves.
For conventional loans, most lenders are going to use item "A" above to determine reserves, and the more months the better. Many jumbo loans these days are requiring a minimum of 6 months of reserves, for example. Conforming loans tend to be more lax, though it is not usually an exact science.
Finally, for purposes of reserves, most lenders will consider either 60% or 70% of vested retirement accounts as well.
Hope this helps. If you need anything else, just let me know.