Fish don't make mistakes.
There are a thousand ways to lose fish. Sometimes losses are unavoidable and the fish is simply too big and mean for you and your space age tackle. But mostly we (the angler) make the mistake that loses the fish.
The most common mistake I see is too much drag. When charter fishing I often get asked questions like, "how hard should I set my drag?" My answer to this varies slightly depending on the situation but essentially you should set your drag so it lets line go before the line breaks - simple.

Percentages
Setting your drag at a percentage of its breaking strain is exactly what I'm talking about. One third (33%) of the breaking strain of the line is a figure you will often be recommended, most commonly as a strike drag for gamefish trolling. This is all well and good as long as a few principles are understood.
You need to use proper drag scales that have a slide displaying the highest reading during your test. String up your rod and reel with line and attach the scales to the end. You hold the rod like you're fishing while your mate simulates a frenzied gamefish running off at high speed, scales in hand. And I mean running! Take off down the wharf, marina or hallway at home. If you have 24kg line, the scales should read 8kg. If not, adjust and repeat the strike. Yes, it can be a lot of fun and games. Just beware of low ceilings as tips may hit the roof should the line part. It is important to load the rod during the test. It is interesting to note how much the drag decreases when the rod is pointed flat. This is the dangerous thing about simply pulling some line off the reel with your hand and saying, "that's about right" - something many of us do! It's very important to pull suddenly and 'run'. If you just slowly pull line off and set the drag this way, when you actually get a savage strike your line could break. This is because of what we call 'start up inertia'. The most drag comes on a split second before the spool slips. Once the correct setting is achieved it may be useful (especially on star drags) to mark the reel with a permanent marker so if you change it during the course of fishing you have a setting to return to.
It might also be beneficial (especially on lever drag reels) to put the lever up to full and test the drag with scales. A slow steady pull will demonstrate how much pressure you can put on if you have to 'redline' the reel, perhaps to lift a stubborn fish near the end of the fight or raise a dead or tail-wrapped fish from the bottom.
Certain situations might require much more drag: big kingies or snapper in very foul ground where losing line means losing fish, or much less: ultralight fishing with one kilo line where virtually no drag would be appropriate, especially on the strike.
The golden rule would have to be 'always err on the side of caution'. After all, you can always put more pressure on later if need be. But once you break the line, 'later' is not an option any more. The horse has bolted.

Don't lose the plot
There is no need to panic if a fish starts taking lots of line off your reel. Be excited! You have hooked a good, if not awesome, fish. But don't lose the plot. I have seen many people bust off the fish of a lifetime because they were afraid of letting a bit of line go off their reel: fish runs and Joe angler cranks up drag to stop fish - fish too big and mean and in straight tug-of-war, Joe loses! This is when I really wish I had a big stick like Rick so I could rap those fingers before they get anywhere near drag lever.

A different kind of drag
Yellowfin are fantastic drag testers. Few fish run as fast and long as tuna. One comforting thought when playing tuna is that there's little chance of getting busted off on the rocks. Usually you have a couple of hundred metres of water under the boat and a few miles around you, obstacle free, aside from perhaps other boats. When a tuna is emptying your reel it's a good time to get excited, take some deep breaths and ready yourself for a fight. When it just keeps taking line and doesn't look like stopping (normally a light tackle scenario) and you can see the bottom of the spool looming ever closer, you have a situation! You may be forced to risk broken fingers and play with the drag.
The pressure of so much line moving through the water, especially when it's going sideways, can cause it to break. Backing off the drag is your best option. Another important factor when you have lost most of your line is increased drag at the reel caused by decreased spool diameter. As line leaves the reel the drag automatically increases. Again, backing off the drag is your best option. Remember: if you're still hooked up, you're still hooked up! Probably, the only time you should lock up your drag is just before you get spooled. Chances are this will break the line, but at least the line should break at the trace knot and the fish won't be left towing hundreds of metres of line. And I promise that under these circumstances I won't break your fingers.
Getting spooled is generally very rare as long as you use appropriate tackle for the fish targeted. I have never been spooled, I just ran out of line once. I hooked a hammerhead shark estimated at 130 kg on a tiny baitcasting set spooled with 150 metres of 6-kg line. The crew did really well, and with good communication and boat handling skills we stayed connected for twenty minutes. The trace was inches from the deckhand's gloves when the shark went straight down and I ran out of line.

Dragging on
As I said earlier, setting your drag at 33% of the breaking strain is 'all well and good'. Unless you have very bad knots or damaged line it will be virtually impossible for the line to break. But sometimes fights just drag on and on and on. Tuna are notorious for this. But let's not blame the fish. The problem we have is at the other end of the spectrum - not enough drag.
For example, we have hooked a really good yellowfin, perhaps 50-kg on 15-kg line. Our strike drag of 33% is working and after an awesome first run we are still connected. But after an hour of hard work we have made no ground. Every time we gain some line the tuna takes it back. The 33% setting (5 kg) is not enough to lift a tuna that is quite happy doing laps around the boat. Should we crank up the drag?
"Don't touch that drag or I'll break your fingers!" Best thing to do is use your fingers on the spool. Hold the spool as you smoothly lift the fish ready to let go should the fish bolt. Your fingers are far more sensitive than any drag washer is. Should the fish run, just let go and the 33% setting will do the job.
Safe as houses.

END