Do people still travel by boat across the ocean?

Yes they still use ships..

Yes.   There is still one real ocean liner crossing from NYC to England.   The Queen Mary II.    Ocean liners are built a lot different than a cruise ship and can handle much rougher water.  

The word is SHIP.

There's only one actual ocean liner in the world. Cruise ships are NOT ocean liners.

Yes, or they did at least until the virus broke out.  You can go from NY to London, or Le Havre, as well as others, (or you used to be able).  The Queen Mary II was one which did that.  I always wanted to do it.  I have sailed on several cruises and I LOVED it.  Actually, I think it takes around five days do the transatlantic and you would want to go on a ship with a lot of amenities, so you have plenty to do, but if you fly over and get on a  cruise IN Europe (or somewhere else) be sure to pre-book your shore excursions in anyplace where it might be a distance from the port to the main attraction areas.  It is also the way to learn the history and really SEE the area!  If someplace doesn't have a lot which you want to see and learn about or the ship offers you a ride into town, you could save your $.  When I have gone on cruises to Europe and the Med and the Black sea, I took a LOT of shore excursions and tours!  It is well worth it.  But, when I went to Alaska on one, and the ports were tiny, and you could walk the area in an hour, and they had inexpensive dance programs, etc., I did that.

Part of the "down in the dumps" feelings I have now, with the pandemic is feeling like I may never get to go do that again.  I had always hoped to be able to!

Most people whose travel plans involve crossing an ocean choose to fly. Those who opt for a ship are usually seeking the experience of a cruise rather than all about their destination.

Yes you can. Go to Cunard Lines for sailings from NY to England.