Not very. I inquired about various mortgage options (refinancing and obtaining mortgage on a new property) about 4 years after Chapter 7 bankruptcy, and I was offered both, albeit at a slightly higher rate (about 3/4 percentage points). I would say it depends on the financial institutions - but what seemed to be of most concern to them was - how far since bankruptcy and financial situation (gross income, indebtness, and payment history) after bankruptcy (mine improved thanks to bankruptcy, so I was told that I should not have any difficulties except a slightly higher interest rate).
No problems getting a car loan - and I receive hundreds of offers of shitty credit cards (low credit limit, exorbitant fees and interest rates) - however I was able to obtain "normal" credit cards (relatively low interest rates 8-13%, no annual fees) with considerable credit limit (not as high as I had before bankruptcy, but comfortable enough to make major purchases if I decided so). Ironically, I cannot obtain the shitty department store cards with 20+% interest rate and a few hundred dollars credit limit - which makes me laugh.
The key is to maintain good payment record before and especially after the bankruptcy so it looks like it was a business decision to cut the losses as opposed to not being able to manage one's finances and payment schedules. For some creditors, bankruptcy is a sufficient reason to turn an application down, but others look at the financial history, and can still give you a loan if it is otherwise good.
Wojtek