Ferries are a really good option in several situations in the UK. If you live in the south east of England, it is a short crossing over the English channel. If there are several passengers in the car, it can be much cheaper than flying. You can take a lot more luggage, especially useful if you have kids. Also you don't need to hire a car on arrival. Check that your insurance covers you for the countries which you will visit and it is a probably a good idea to buy breakdown cover. I would recommend taking your car if your destination is not too long a drive from your arrival port. It's a good idea to buy European breakdown cover if you decide to take your own car.
Once the ferry crossing becomes longer, e.g. to Santander in northern Spain, the cost of transporting your car can become high. It may be cheaper to fly with a low cost airline to Bilboa. Whereas on a short crossing ferry to France it can be very cost effective to take your car. There is also the risk of sea sickness on longer trips. I had a very rough overnight crossing from Holland to Newcastle over the North Sea one Easter. It took me 2 days to recover from this.
A ferry crossing is a great way to visit the Scottish Islands. There is not much public transport on the islands, such as the Hebrides, Orkney and Shetland, so you will be able to see a lot more if you take your car over on the ferry. Some of the roads are single track and full of sheep, so your progress will not be fast but there will be plenty time to see the scenery. You can also do a day trip as a foot passenger if the island involves a fairly short crossing, e.g. to Mull from Oban.
The crossing from the UK to Ireland is fairly short and could fit in well with a touring holiday of the UK and Ireland.