While mortgage lenders have certainly tightened up their lending criteria across the board, individual lenders all still have their own criteria for qualifying potential borrowers.
For housing expense ratios (the ratio of your your mortgage payment or PITI to your monthly gross income), Freddie Mac is still quoting the 28%-31% number that you mentioned. But this is only one factor and is evaluated in context with the rest of your application.
Another common ratio used is the debt to income ratio, which is the ratio of your total monthly debt payments, including your potential mortgage payment, to your monthly income. This again varies by lender and loan product, but should usually fall in the 30%-40% range.
Your credit score is another obvious factor and one where lenders have noticeably tightened up . Before the housing market troubles, a 690 FICO score could probably get you a prime rate mortgage with some lenders and a 720 would with nearly all (provided you meet the other requirements). Now, many lenders are requiring a minimum of 720 and some require 740 or 750 to qualify for prime rates on conventional mortgages.
The other major factors in qualifying for a mortgage are income, job stability (including what industry you work in), the property you want to buy (it's value, particularly the Loan-to-Value ratio), and what kind of down payment you plan on making.
Mortgage applications are generally looked at as a whole, and different lenders and loan products all come with different criteria.
For more information on homeownership, you may want to check out the HUD website at www.hud.gov or www.freddiemac.com.