If I sell some of the stocks I owned that have lost a lot of value, would I be able to write-off these losses?
Harvesting tax losses by selling securities that have declined in value can make sense if you have or will have realized gains, provided that transactions costs are not significant and there are other, comparable or better investments that you can make with the proceeds.
If you do not expect to have realized gains, your realized losses may be carried forward except for $3,000 per year that can be written off against ordinary income. Make sure that you do not run into a "wash-sale" problem by repurchasing the same or substantially the same securities within thirty days of the sale. You should consult with a tax professional and/or your financial advisor to confirm the tax implications given your particular facts and circumstances.
I agree with Mr. Dowd. Also, there is always some other investment to replace the sold ones. Thus, don't get into the trap of holding on to loss positions because "they may go up in value". Transaction costs today are negligible, with firms like Fidelity charging only $7.95.