Is old wine safe to drink?

The simple answer is drink it. People have bottles of wine that have been saved since the 1920s or even before that, that they treasure and drink on special occasions. Wine is an alcohol. The alcohol keeps bacteria and other nasty things from growing in it. You are generally safe in drinking it.

A separate question is will you enjoy drinking the wine. Only certain wines were meant to age. Most wines are not meant to age. If you have a "touristy bottle" like a Chianti-in-a-basket or a Portuguese-wine-in-a-basket, those were never sold because they were tasty in the first place. They were sold as decorations, really. White Zinfandels were meant to be drunk immediately, not even aged for more than a year. There is a gigantic percentage of wine bottles that go old in a year or two, never mind decades.

Even for wines that were meant to age - say fine Burgundies or Bordeaux wine - they only age well when stored properly. They need to be at an even, cool temperature. They need to be on their side, so the cork doesn't dry out and let in air. They need to be kept away from sunlight. You could have the most perfect bottle of wine for aging and still have it taste awful because of bad storage conditions.

Still, even if the wine was ruined, it won't kill you. It'll just taste like vinegar.

Open the bottle. Even if it's not tasty, it's still an adventure to taste a wine from that era.