What is the 3rd wedding anniversary gift? The traditional theme for 3rd anniversary presents are leather gifts; however, if you like to follow the modern themes then it is crystal or glass. At MyGiftGenie we are slightly more traditional which is why we have selected a range of amazing leather themed gifts for him, her and couples to celebrate your 3rd wedding anniversary. Find leather gift ideas from personalised wallets, stylish belts or trendy bags. If you are searching for crystal anniversary gifts then please browse our 15th anniversary gift selection as this is the tradional 15th theme. Happy 3rd anniversary.