There are numerous ways to test if your knife is sharp. This writeup mainly refers to kitchen knives, though you can also try these techniques on your bayonet/bayonnette, bowie knife, hunting knife, Swiss Army Knife etc.

1) One of the safest and most effective ways requires a ripe tomato (or a piece of tomato) with its skin on. All you do is place the sharp edge of the blade of the knife against the skin of the tomato and gently cut. Do not use any downward pressure on the knife other than the weight of the blade itself. Move the knife fowards or backwards about 1cm or so (half an inch) and if the knife actually cuts the tomato's skin, then your knife is sharp. This is a very handy method if you happen to be cooking something that involves tomatoes at the time. A blunt knife will just press/mash the tomato.

2) Slightly more dangerous, but the method I prefer, and from what I gather many culinary professionals use this method too. Do the tomato test on your thumbnail. Only move the blade a very small distance (half a centimetre, 1/8th of an inch) and if the knife "sticks" or "catches" in your thumbnail, then your knife is sharp. A blunt knife will just slide across your thumbnail and won't cut. PLEASE BE CAREFUL with this one folks. Use virtually no downward pressure and only move the knife the tiniest distance. Be aware that some knives will have sharp and blunt areas, so if you zing across your thumbnail with a knife that you *think* is totally blunt, you may be in for a nasty surprise.

3) Cutting a piece of paper. Favoured by a lot of samurai movies I have seen, just take a piece of paper (rice paper if you're a samurai, photocopier/printer paper if you're in the office), hold it by one edge only, and use your knife to cut downwards on the free edge. A sharp knife will cut, a blunt knife will not. This not the best method, as even fairly cruddy knives can achieve a cut.

4) Shaving your arm. Not the best method, a fairly blunt knife will shave you if you cut with the grain of your hair. Other disadvantages are:

The requirement of hairy arms/hands.

A small bald-patch on your arm.

Hair all over your knife.
I've also heard stories about teachers/employers/counsellors seeing bald patches on peoples arms from testing knives and assuming they are deranged psychos, then sending them off to counselling.

5) Shaving your face.
Advantage:

You look really cool and manly like Crocodile Dundee
Disadvantages:

Only works if you have facial hair.

Hurts, can leave shaving rash.

Will blunt your knife.

End up with whiskers/shaving cream all over your knife.

6) Just use it.
If you use your knife enough, you'll end up being able to tell just from using it whether it is sharp or not. If it isn't, just grab your sharpening steel and give it a few slides. Many professional butchers/cooks don't even bother with any of the above methods, they just know by the feel of how their knife is performing.

If you do not have a tomato or piece of paper handy (which some reckon, will help blunt a knife designed for cutting other things) and don't want to shave patches off your arm (ditto) or risk slicing your thumb(nail) in two then it is possible to test the sharpness of a knife safely using only your thumb, as long as you remember this golden rule:

Never rub your finger ALONG the edge of a blade - rub it ACROSS it.

. The easiest way to do it is to turn the knife upside down then move your thumb across the blade once in a side to side motion. You are testing to see how thin that edge is where thin equals sharp. You should soon find it easy to gauge the sharpness of a knife without risk to life or limb.

The best way for testing if a knife is sharp enough is usually to try and use it for its intended purpose. Assuming you have an idea what you're doing, you will quickly find out.

There are, however, several test which can be used to test a blades sharpness. My favourite, which I use on my straight razor from time to time, is the hair test. Get one of your hairs, hold it from the root end (I don't actually know why you're supposed to do this, but it's what I've been told to do, and so what I'm used to doing - I suspect it's so there's less weight bearing down on the edge), and gently move the hair down from about an inch or so above the blade. If upon contact with the edge, you hear a pleasing little *zing* and stand with a shorter hair in your hand, you have a very sharp blade. A blade that is able to cut the hair if you sort of pull a bit down with your hand as the hair touches it is still quite sharp, and I have no problems shaving with one that cuts the hair if I do gentle swings directed at the hair either.

The fingernail test is another one. Wet your thumbnail (it is the thickest and toughest nail on your hand, and so is the safest, though I have never experienced cutting very deep into the nail), for example by licking it, then gently slide the blade of the knife over it. The most important thing you'll learn from doing this is whether your edge is alternating between dull and sharp, or have small chips in it. You'll be able to feel the change between dull and sharp, though you need some training to judge how sharp it is. I can't really do this. Chips in the blade will tug on your finger, and depending on intended use, can be really detrimental to its function (you can get away with pretty awful chips for some uses, but, say, the aforementioned straight razor will probably be hell to use - no direct experience, really, just guesstimating).

You can also use the other side of your thumb, sliding it across the edge (not along it!) back and forth to judge sharpness. You'll feel chips this way as well, though maybe not the smallest ones, but again it takes some training to accurately judge how sharp the blade is. Judging if a knife is sharp enough for kitchen use isn't too hard with this method, I find, but I can't feel if an edge is keen enough to shave with.

The tomato test is really quite nice on kitchen knives. It's a good gauge of sharpness for their use, and is done by trying to slice a tomato with the knife without using any pressure. Just lightly touch the knife to the tomato and move it a short distance - if the skin is cut through, the knife is sharp.

As a sort of postscript, I want to mention that there are a number of different visual tests, possibly somewhat more objective than most of the above. I suspect these are better observed than explained, so if you're really interested, go check out Youtube for something like "straight razor sharp test". It should actually get you the video I first saw about these visual tests.