Which type of onion causes the least eye irritation
The onions that cause the least tears are those with lower sulfur content.  But it turns out that it's not just the variety of the onion that's a factor, but the sulfur content of the soil they're grown in (eg, areas of Georgia, where Vidalia onions are grown).  Of course, this means they don't have the same 'bite' as you'd get from other onions.

In the U.S., at least, they're typically sold as 'Sweet' onions.  They may go under names such as Vidalia, Maiu Sweet, Mayan Sweet, Walla Walla, etc.  They tend to be yellow varieties, but they're fairly obvious in their shape-- they're not round, they tend to wider than the length from the ends.  They also tend to be more wet than regular onions, so they don't store as well, and thus have a shorter season (or they're flown in from South America, for those of us in the U.S.)

If I were to rank them, from least to most tear-causing, I'd say:


sweet onions
green onions / scallions
red onions
other yellow onions
white onions