does spoke count have anything to do with strength of the wheel? i've been riding a 20 spoke in front and a 24 in rear, and it has been fine, got a differant bike with corroded nipples and the same spoke counts and the front spoke snapped. now looking into different wheels, found a great deal, but it is a 18 spoke count front and 20 spoke rear, and it makes me hesitant to buy them, especially if spokes/nipples are going to constantly snap.
Yes it can. Less skilled wheel builders often compensate for their lack of skill with more spokes. ;) The most important thing with wheels is the skill of the wheel builder. I've owned a set of 16 spoke wheels for over 10 years and a ton of miles (I run between 230-250lbs and ride as much as 10k miles/yr) . Just this year the rear broke it's first spoke so I had the whole wheel re-done. I expect it to last more than 10 years this time (I don't use it as much any more :))
The wheels with corroded nipples probably need to be replaced or rebuilt. If you buy the 18/20 spoke wheel set I would ride them for 100 miles or so then take them to a good wheel builder and have it retensioned. You should then have a wheel that will last for a good long time.
Yes, spoke count is important to wheel strength. The spokes are what support your most of your weight, not the rims (though the rims do add rigidity). To support your weight, the spokes need adequate tension...otherwise they will go through a more severe compression / expansion cycle each time the wheel goes around, leading to metal fatigue and spoke failure. If they have enough tension, they will not compress as much. With more spokes, the required tension from each one to adequately support your weight is less, so there is more margin for error. Thus you can get away with a sloppier wheel build with more spokes. But if you have less spokes, each one needs to have higher tension. Spokes (new ones anyway) have a very high tensile strength and are stronger than the rim, so the danger of overtightening them is that they can crack your rim. Rim manufacturers specify the maximum tension that is safe for their rims.
Spoke count for many riders is related to weight.. I have 2 wheels - a Mavic Aksium and Velcoity Aerohead and the Aksium which is 24 spoke rear wheel is 30 grams heavier than my 36 spoke Velocity Aerohead..
The 36 hole aerohead was built up with 14g straight spoke and brass nipples and still came in at 950 grams.. Sure you can buy something lighter by 100-200 grams but you will be giving up a little bit in overall strength..
There are some lower spoke count wheels that are in the $1500+ range that are just as stiff but you pay a premium for those wheels.. I have a set of eurus that I use on fast training rides and centuries but most people are just looking for a solid everyday training wheel..
The other thing to keep in mind is the repairability of a low spoke count wheel when a spoke does break - I'm talking about a field repair, getting the rim true enough to ride slowly back to your car or a bike shop. With a 32 or 36 spoke wheel, you're a lot more likely to be able to wrap the broken spoke around a nearby spoke and limp in. When I broke a spoke on my Neuvation wheel (24 spokes, 27mm deep rims) we couldn't true it up enough to ride on and I needed to hitch a ride. Even with the rear brake caliper opened up all the way, the rim was still rubbing in two places (one on the left, one on the right....). Fortunately, it happened right after the end of the Tour de Tucson, when a stupid recumbent rider (apparently going for a PB) crashed hard into me while I was lining up to turn in the timing chip. I didn't fall, but everyone around me heard the crash. There were lots of friends around, so getting a ride back to the hotel was not a problem.