"My father recently passed away in the beginning of June 2006. I then moved back home to live and support my mother in July 2006 since she's a housewife and has no income. Would I be able to file as "Head of Household" for 2006? And can I file my Mother as my dependent for 2006? Please advise. Thanks in advance."
Sorry to hear of your loss. For 2006, your mother will be filing as "Married Filing Jointly" -- yes, she will be filing jointly with your father. There are a couple of formalities you will need to follow with the IRS. These are spelled out in the short article, Death of a Taxpayer.
If you meet the criteria for claiming your mom as a dependent, then you would claim her as such on your tax return. And she won't claim her own personal exemption on her tax return.
If you are unmarried and you paid more than half the cost for supporting your mom for the year, then you could file as Head of Household. See all the rules in IRS Publication 501.
Next year may be a good time to hire a tax professional. They can review your and your mom's situation and figure out the most advantageous way for you to file your returns.