1. What are the most durable laptops?
2.Of Fujitsu, Toshiba and Samsung, which is the most durable?
I repair and replace laptops all the time for my clients. There is only one truly durable line of laptops and that is the Panasonic Toughbook. The rest will not take abuse, and most will go belly up withing 2-3 years even if not abused. The only problem with the Toughbook is the price, but you get what you pay for.
Miltope RCLC-2 http://mymiltope.com/pdf/datasheets/MyMiltope_RCLC-2_Datasheet_w.pdf
I bought an HP Elitebook 8560w 3 years ago, it's pretty solid. Survives 100cm drops easily.
Lenovo, as Jan suggests, is built for more durability on the daily business use end, but the Panasonic Toughbooks are actually among the most durable laptops money can buy, but also at the cost of heavier weight and typically a little lower specc'd than other laptops, especially within the price range.
Fujitsu actually builds their laptops for better durability among the brands on your list, though their customer service may not be the best. Toshiba has gotten better over the years, both with build quality and service. Sony, unfortunately, hasn't been producing laptops to the best of their ability (not as much as is seen in their Xperia Z phones), and I have seen and read an increasing amount of software issues that are slow to be fixed or patched.
Best advice is to gather your wants, then your needs, and then your price range so that you can find laptops within your price range from each brand. Read the reviews for each laptop, and compare them with each other. Narrow the list down to the ones that meet or exceed your requirements and wants. Compare again, and include reviews with the comparison, until you choose a laptop you can live with. You might find that Fujitsu is more durable, but Toshiba may be better overall due to decent durability and better customer service.
As Oron explained it really depends on what you are looking for and what you are willing to pay. There is a multitude of devices on the market advertised as rugged or semi-rugged that meet certain durability criteria up to MIL-STD (military specification standards)
However, if you are looking for a device to play games on most of these rugged or semi-rugged devices won't come even close to fulfill your needs. Usually you can get a "consumer" targeted device with the same hardware specs for a third or quarter of the price.
Outside the (semi-) rugged range the most durable laptops are probably the Lenovo Thinkpad (X&T) series. These devices have proven to pass a lot of the tests performed by (semi-)rugged devices. But again, they have a higher price tags than your average entertainment laptop ~ often even above laptops designed for games.
So, to answer your question:
1. That would be the Lenovo Thinkpads in my opinion.
2. Out of the three I would say probably Fujitsu? While generally underrated, they actually have a very high built quality and a very good durability across all their laptops.
But before buying one check in with the store about their service/warranty procedure for Fujitsu devices. That's an area where they can be a real pain.
1. This is largely a question of a particular range of laptops (and prices!) rather than just the make. For example, Panasonic make a range of very rugged laptops called Toughbooks, but they're not cheap!
2. The same general point applies to this question as to (1) above. Those companies may a range of models described as "business laptops" which are much more robust than other laptops (and more expensive!). Toshiba's business range of laptops are called Tecra and they are very resilient. Fujitsu business range are called Superior LIFEBOOK and Samsung's go by a variety of names but are listed as "business laptops" on their web site. Of those three makes, I only know Toshiba's laptops well, and the Tecra range are certainly very well made.