We let the kids be naked at home and encouraged use of the toilet from about 18 months on, but we didn't do any formal training. They all "took" at their own pace and in their own time. DS#1 was daytime trained at about 2, more or less. Probably about 20-22 months, but since DD was born at his 21 months, we didn't want to pressure him on that with the new baby. DD refused to use the toilet until one month after turning 3, and she simply decided one day and that was it. DS#2 was in the middle.
There were some accidents of both types, but we never made a big deal about any of it, either positively or negatively. And they are all using the toilet just fine now, at ages 8, 6, and 4.
DH comes from a family that strongly encourages early training (his mom had them crawling to the toilet to use it before they could walk, and SIL followed that advice, so her two were both under a year old). Based on the kids I've seen in his family, they are no better or worse than kids who waited until age 4, so DH and I figured that low pressure was more important than saving money on diapers, wipes and whatnot.