Your question has a lot a variables to it, credit rating, current employment status (how long there etc), current level of debt the term of the mortgage (20 years, 30 years.)
General rules of thumb would be the more of a down payment you make the lower the interest and monthly payment.
Some general figures so you can compare how your payment varies with a 1% interest change.
With 10% ($30,000) down at 6.5% for a 20 year note payments would be $2,013.05 a month. For a 30 year mortgage with the same down payment and rate it would be $1,706.58.
Same conditions at 1 percent more, 7.5% would be $2,175.10 monthly paymets for a 20 year note or $1,887.88 for a 30 year mortgage. With the fed continually dropping the interest rate you should get an offer higher then 7.5% unless you're a bad credit risk -- lenders are nervous due to the subprime mortgage crisis.
So that 1% difference costs over $150 every month for the life of the mortgage.
Typically mortgage companies/banks get hesitant if your monthly payment would be more then 25-30% of your gross monthly income. Though if you have a high debt load they may want your housing/income ratio to be lower.
Look at your savings and other liquid assets, leave enough for a 6 month emergency and see what you left have for a down payment. The larger the down payment the better for you in the long run. It reduces the amount you borrow and gives you a significant savings on your interest over the course of the loan.
Avoid balloon payments and adjustable interest rates, that's what's hurting a lot of people now.
I disagree with the advice to never take a 30 year mortage. If an attractive fixed rate is offered you should consider it should rates go lower you can always refinance if they don't you can always make additional payments directly against the principle to reduce the interest you pay. Interesting side note, if you get a 3% raise at work each year after 14 years your making more then 50% more a month then you do now, yet your housing cost is unchanged)
Additional tip, shop arround -- do not assume the bank you've been using forever will give you the best rate.