When filing My taxes, can I claim my 21yr old son, who is unemployed, his girlfriend who works part time and goes to college part time and their daughter, who all live with me?

You can claim your son as a "qualifying relative" as long as (a) he made less than $3650 in net income in 2009, (b) you provided at last half his support, and (c) he doesn't try to claim his daughter as his own dependent. You can claim your grand-daugher under the same criteria, but only as long as neither of her parents claim her as a dependent on their own tax return. And you can claim your son's GF as "qualifying relative" only if (a) she lived with you all year, (b) her net income is less than $3,650, (c) you provided at least half her support, and (d) she doesn't claim her daughter as her own dependent.