Yes you can, if you are able to itemize deductions. The lending institution will report the interest and points paid to you (and the IRS) on a form 1098-mortgage interest, which you can use to prepare your taxes.
Again, you have to itemize for it to do you any good. You would itemize if your interest (and other items on Schedule A) exceed your standard deduction. The standard deduction for 2006 is $5150 single ($10300 if married filing jointly). If single and over 65 it is $6400 ($12,300 if married with both over 65). The standard deduction goes up roughly by inflation each year.
I'm not a tax professional. For some reason my wife doesn't understand (nor do I) I do volunteer tax preparation, the source for the above info.