You can get chafing for two reasons:
1. Mechanical chafing - this is where a seam a bit of material, or something else is rubbing against you. Enough rubbing of anything, and eventually it'll damage the skin below. Solutions: Bike specific shorts go a long way towards fixing this usually, if you've got particularly hairy 'nads running a clipper set to #2 around the area (don't shave - the hairs growing back in will cause problems) will also reduce the amount of rubbing going on. Chamois cream can also help, because it's a lubricant and will minimize the effects of rubbing.
2. Infection related chafing - Your 'nads are naturally a somewhat unsanitary place (why God saw fit to put the pleasure center next to the waste removal area I'll never know). Add in hot humid weather, occasional rain, a whole lot of sweat, and all the dust/crap that gets kicked up off the road and into your general ass area from your rear tire . . . and it's even worse. There's always going to be a small amount of rubbing going on when you're sitting on a bike saddle, even if you've religiously followed all of item 1 . . . and bacteria can and will cause skin irriation. This ranges from red itchy skin to red bumps, to pus filled blisters . . . which pop and then you'll have open wounds in this unsanitary area. Cycling is gross.
You want to keep your undercarriage as clean as possible at all times. I always shower and wash my 'nads before a long bike ride. Most chamois creams are antibacterial . . . which is another reason to use them for long bike rides. Don't wear bike shorts more than once before washing them*. When you get off the bike, don't chill in your bike shorts - a wet body temperature chamois is a bacteria growth chamber. Get them off as soon as possible and shower. After your shower, make sure to carefully dry off your undercarriage completely before putting on undewar. Wear loose fitting cotton underwear - no synthetic materials. Synthetic materials also seem to encourage bacteria growth.
* I give shorts for commuting a pass on this . . . you can wear the same pair to work and then back home from work. But try to put them somewhere where they'll dry out completely before you put them on to go back home. Never wear the same pair more than one day of commuting though.