What is the lowest and highest credit score ?
Essentially each person has 3 credit scores. This is because there are 3 recognized credit repositories. Each has their own proprietary formula that your credit information is fed into, resulting in a credit score. Because each formula is different, each repository will have a different score for you, although they should be closely related. That being said, the score answer to your question is that a score can range from 300 to 850.
While this is the score range, after viewing a few thousand credit reports, I have seldom seen a score in the 300's, much less as low as 300, and have seldom seen scores higher than 830 or so. That is because, while the formula may allow for an 850 that would be a statistically perfect credit profile. Even if you have always paid every bill on time, and never had a late payment or derogatory item, that doesn't mean you will have an 850. Credit payment history accounts for only about 1/3 of your credit score. Other items such as length of time the accounts are open, types and number or credit accounts, and balances versus credit limits all play a role as well. Because of this, in conjunction with the fact that each of the bureaus formulas is private, makes an 850 essentially impossible.
Even with the tightening of credit over the past 24 months, a score of 740 or higher will normally qualify you for the best rates and terms available. This is up from 700, and then 720 over the past 6-8 years or so. Additonally, while 620 used to be the low end cut off for most 'conventional' type of rates, we now see 640-660 as a minimum. You can also count on some sort of pricing hit to your mortgage rate if you fall between that 640-660 range on up to 740, as it is not until the 740 mark where you will see the best interest rates available.