A test in the print magazine Fly Fisherman showed the Trilene and the Orvis knot to be equally strong and on top of that said that they were able to maintain 100% of the line strength. I really have my doubt if that will hold for all types and thicknesses of line, but still it does prove that these could be the knots of choice for the concerned fly fisher.
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Fly attachment knots
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Palomar knot
A knot that is easy to tie and has a good breaking strength of over 90%. It can be difficult passing the line twice through the hook eye, but pass the tag end though one way first and then back. Then make the loop as small as possible and pass it over the hook. Tighten by first pulling both ends - then the tag end alone.

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Surgeons loop
A loop which can be used to tie on small flies or flies that need to work on the leader. The knot is strong, but the open loop is a bit fragile where the fly wears it, so the knot ought to be inspected and retied regularly. Make sure you do not tie the loop too large as it and the knot has a tendency to grab any material on the fly and lock. This will often lead to a fly swimming backwards...

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Duncan loop
The classical loop for flies that need to work freely on the tippet. Fairly easy to tie and can be tightned according to taste.

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Orvis knot
Can form a loop that tightens when under strain. Its strength almost compares to the Trilene knot with a 95% avarage.

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Figure 8 loop
An easy-to-tie loop that leaves the line and eye in a straight line. It is a bit difficult to tighten in a manner that results in a small loop. A too large loop will often catch the fly or some material and leave the fly fishing sideways or backwards. The figure 8 loop is also great for making loops on leader butts and tips and good to use on tippets if you want a loop-to-loop connection between tippet and leader.
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Trilene knot
The breaking strength is very high for this knot; very close to 100% for some lines and diameters and almost always above 90%. Do not cut the tag end too close. The knot has a tendency to untie itself after many casts.

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Mörrum Guiding knot
A guiding knot well suited for up or down eye flies on heavy tippets especially salmon flies. The knot is easy to tie with a good breaking strength. Tighten the loop section first and then work it slowly to a position in under and almost in the hook eye. The direction of the tippet will be at an angle to the eye, and hence the knot is no suitable for straight eyed hooks. On up- and down eye hooks on the other hand, the tippet will be parallel to the hook shank, and guide the fly nicely in the water.

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Improved clinch knot (not recommended)
This is a very common knot, but even though it seems to look much like the Trilene knot, it's very weak in comparison. Down to 60% breaking strength in some cases. I do not recommend using it.
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Leader knots - mono to mono
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Blood knot
A knot used to tie two monofilaments together, i.e. tippet to leader or two pieces of a knotted leader. The knot is a bit difficult to tie, but can be tied without tools with some practise. It is compact and has a high breaking strength and leaves the line absolutely straight. The number of turns can be varied, but 3-5 turns work well on most lines. Cut the tag ends very close to the knot.

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Surgeon's knot
This knot is normally used to tie two monofilaments together, i.e. tippet to leader. The knot is fast and easy to tie and has a high breaking strength. It does require one side to pass through the loop and is more bulky than the Blood knot. It also leaves a small angle on the line. The number of turns can be varied, but two turns work best on most lines.

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Leader knots - mono to fly line
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Needle knot
An excellent knot for attaching the leader to the fly line. It yeilds a very neat, straight and strong transition between the monofilament leader and coated fly line.
It requires that you pass the mono through the core of the fly line by poking a hole with a needle. Cut the leader at an angle with a pair of scissors to make this process easier. Pull 10 centimeters or 4 inches of leader butt through core and out through a hole in the side of the fly line coating and tie the knot.
PS: I previously named this know a nail knot, which it's not. Sorry.
- Martin

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Nailless nail knot
An fine knot for field attachment of a leader to the fly line. It is almost as straight and strong as the above nail knot, but can fail if the coating is pulled off the fly line core.
The advantage is that it does not require tools other than a line clipper. Lay the butt of the leader along the fly line with about 10 centimeters or 4 inches overlapping. Fold 3/4 of the tag end of the butt back towards the end of the fly line and fold it over and around the whole assembley in 4-6 tight loops close to the end of the fly line, working your way back towards the loop formed by the mono. Hold the loops tightly between your fingers. Pass the mono tag through the loop and moisten the whole knot before tightning the mono. Work the knot slowly together arranging the loops nicely. Tighten by pulling both ends of the mono. Do not pull the fly line before the knot is very tight! Trim the lines as close to the knot as possible and test with a firm pull in fly line and leader.

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Submitted January 30th 2010
nail knots are a breeze if you pull the thin end of the leader through first, starting a short distance up the line from the end. Pull through till there is enough of the butt end of the lelader left to make the knot and proceed.