I live in Ireland and I know you can get a ferry to Britain and to mainland Europe but is it possible to get a ferry to the United States or Canada?
Nope. Closest you could get is the Smyril Line ferry, which will get you as far as Iceland. After that, well, how well does your vehicle float…?
No. You can get onto a ship (and have your car loaded on board as well) to travel across the Atlantic, but it would be an ocean-going vessel with a much more complicated loading/unloading process. Ferries are designed for short trips in relatively sheltered waters, and even the big Baltic and North Sea ferries would probably not survive the first North Atlantic gale they encountered.
If you are just talking about regularly scheduled trans-Atlantic sea travel, as opposed to the typical walk on/drive on ferry loading using specially built ships with opening bow/stern doors, then this used to be the common way to cross the Atlantic up until air travel became common and affordable enough to put the ocean liners out of business.
As others have pointed out, there don’t seem to be any purely passenger lines operating any more. However, it is possible to book passage on freighters. Most freighters have room for a few passengers, and apparently the accommodation is quite good – comparable to a nice hotel room – and you get to dine with the officers. Last I checked, travel time was something like 10 to 14 days, and prices were around $1200. You can get more information on this lovely website called The Internet Guide to Freighter Travel.
I had the notion of eschewing air travel the next time I visit my gf in the US but it doesn’t seem at all practical. 
oh well.
That’s why you take a side trip to Cuba beforehand, to get one of those 50s cars that has been turned into a boat.
From time to time the pleasure cruse lines have one-way transatlantic cruises. These cruises are not intended to provide regularly scheduled service, but if you’ve got the time and money, and the cruise is happening when you want to go, why not? They might even let you join the ship at the last European port before the open ocean, so that would be tantamount to an ocean voyage in the old days.
You could look into that.
If you take the widest possible definition of a ferry, i.e. a regular service for transporting passengers and goods across a body of water then yes, you can get a ferry across the Atlantic. Just go to an airport and get on any of the transatlatic airplanes that leave every day.
If you mean a ferryboat then no. However, the difference between a ferryboat and an ocean going vessel gets pretty small. I would expect a ferryboat that goes from Ireland to mainland Europe would be a pretty seaworth vessel and, except for the matter of carrying enough fuel and other supplies, could probably cross the ocean…
Ok I have a supplimentary question. Are there environmental advantages to putting to sea instead of flying?