I'd like to give the following white wines as a (re)gift. Are they still good? A 2001 & a 2003 Sancerre?

I would not give these wines away as a gift. Sancerre are very nice wines made from the Sauvignon Blanc grape. If they were stored properly, that is, in a wine cellar or a wine fridge then they may be still drinkable, but I doubt that is the case here.

They are very inexpensive (under $10) so I would just uncork them and feed them to your kitchen sink drain.

If they have been properly stored then there is a good chance they are still drinkable.

However, most whites only last a couple of years before they start to deteriorate there are some though that will keep for years.

To be on the safe side I wouldn't give them as gifts, but would definately crack them open and try them myself.

White wines do not store as well as dry reds. No matter how good a vintage they are they can become vinegar-y or corked. Most vineyards recommend that whites be consumed with two years. I wouldn't give it to anyone.