Not much to add to the posts so far, except details:
First of all, the original poster said he is a helicopter pilot. I've never flown a helicopter, so I may be wrong, but I believe that the direction of the yaw in most western aircraft is opposite to that experienced in helicopters. (Although eastern block aircraft usually have the propeller rotating the other way, so the yaw in these aircraft is the same direction as a helicopter.)
There is more yaw at low speed. (I don't think this is true in helicopters - but I'd be interested to know if I'm wrong...) This is because the yaw is caused by the rotating slip-stream off the propeller hitting the side of the vertical stabiliser - i.e. hitting the vertical stabiliser with an angle of attack. When stationary, this angle of attack is quite high. When moving at 100kts, though, you have to do some vector arithmetic to add the prop slipstream to the free air, and the total angle of attack is quite low. This is the reason why many pilots only notice the yaw on take-off, or when entering a steep climb - both of which are low speed, high power manoeuvres. Also, the rudder is less effective at low speed (less airflow over it) so a large amount of rudder input can be required. It is noticeable when cruising, but not as much.
I don't think the thrust line being to the side of the engine, which distaff-beancounter is talking about, is relevant in most cases (but see taildraggers, below!) This effect is called p-factor, and only applies when the aircraft has a positive angle of attack. Once the nose of the aircraft is pointed up, the angle of attack of the down-going blade is slightly higher than the angle of attack of the up-going blade, and so very slightly more thrust is produced on this side. (Very hard to visualise, but if you think about it long enough, you'll see it's true.) As with the slipstream effect, this is more noticeable at lower speeds - once the aircraft has a bit of speed, the result of the vector sums will show that the difference angle of attack between the blades is minimal. This is true of singles as well as twins, and is rarely noticeable in a tricycle-geared aircraft (which has a zero angle of attack until it rotates at a fairly high speed). I think the reason you get more yaw in a twin is because you've got more (double) the horsepower. The actual effect would be slightly less than double, though, because the engines aren't directly in line with the vertical stabiliser, as the engine on most singles is.
Taildraggers... The slipstream effect in a taildragger is exactly the same as in a tricycle. There are several reasons why taildragger pilots are more active on the rudders - but propeller slipstream is not one of them. First, p-factor is relevant, because the aircraft is at a very high angle of attack at the start of the take-off roll. When the tail is raised, the p-factor stops being relevant, but you will get gyroscopic procession during the period when the tail is being raised (but not once it has been raised). Finally, having the centre of gravity behind the main wheels means that the aircraft is unstable, and every minor excursion must be actively corrected - whereas in a tricycle, the aircraft will pretty much keep itself going straight (the same way a car will straighten itself if you take your hands off the wheel).
Of course, the pilot isn't actually aware of any of this as he flies - he just applies whatever control inputs are required to keep the aircraft straight.
And finally - radial engines. I'm not sure about extra yaw with radial engines, but there is definitely extra yaw if you're lucky(???) enough to fly an aircraft equipped with a rotary engine - one of those antique eccentricities where the whole engine rotates about the crankshaft. The engine has a huge amount of angular momentum, which results in the engine trying to twist the aircraft in the opposite direction. (All engines do this, but the extra momentum of the rotary engine means it's (apparently) actually noticeable.) In flight, this will be noticed as a roll to the left. On the ground, the rolling effect will force the left wheel onto the runway, causing more friction on the left of the aircraft, and therefore a yaw to the left.
And the disclaimer - I don't really know what I'm talking about, and the information in this post is my own version of things I've read or picked up along the way. I could well have got some of it (or all of it!) wrong, so I'm waiting for corrections...
Hope that helps!
FFF
-------------