Most lenders require an inspection -- there is a place in the contract where the party who will order/pay for the inspection (usually $35-65) is defined. Sellers are frequently asked to do this unless the buyer is more comfortable being in control of this process. If infestation of termites (or other insects, e.g. carpenter bees) is found, the VA contract requires the seller to pay for treatment and repair any damaged wood.
If a house is bought with cash the buyer may still ask for a termite inspection -- and would be wise to do so.
If the buyer is purchasing an "as is" property, e.g. a foreclosure, short sale or estate sale, his lender will probably still require a termite inspection, but the seller will not be liable for any treatment or repairs if any infestation is found. The buyer should include an inspection contingency so that if an expensive situation is found, he can choose to correct the problem himself or walk away from the contract.
Bottom line -- if you're a buyer, always ask your lender about a termite inspection requirement upfront so you'll know how to negotiate that in your offer to protect yourself. If you're a seller, know that unless you're selling your home "as is" the state of VA will require you to deliver a termite-free home to the buyer. And, everyone should get the inspection early enough to leave enough time before the settlement for treatment and repairs should they be necessary. The lender will want to see evidence of that before closing.