Yes. If the amount is over $600 they are supposed to issue a 1099-MISC.
The amount you report as income is the fair market value of the prize. This may not be the amount listed on the 1099-MISC, but that's ok (although the IRS may send a letter asking for an explanation later.)
For example, if you won a sofa with a "list price" of $2000 but the store always has it "on sale" for $1199, then $1199 is the value of the prize.
If you report a value different than the list price and different than on the 1099-MISC (if you get one), you should keep proof of how you determined that the value was different. Don't send it with your tax return, but keep it in your files in case you are asked.
