Judy

I can not offer a scientific explanation for what you have observed. 
Personally I suspect you are seeing patterns in random noise. That is, it 
is unlikely that a light will turn itself on when you walk past it, so it 
is a shock when it happens. If this should happen a few times 
consecutively then it appears some mechanism is at work. Science has been 
dogged over the years with precisely this prolem. It is why all scientific 
data must be absolutely reproduceable and repeatable by independant 
observors. The human mind appears to be very good at seeing order or 
patterns where there is none. In the interests of finding an explanation 
to your question I would suggest applying the scientific technique to this 
phenomena you have observed and do some controlled experiments. 

In order to rule out random chance or coincidence do lights ALWAYS turn 
themselves on whenever your children walk near them. To test this turn off 
a light in your house and have one of your children walk near it. Does the 
light turn on by itself. If it does, repeat the procedure as many times as 
possible doe sthe light ALWAYS turn itself on, when you are happy this is 
repeatable have your child approach the light slowly until it turns on. At 
what distance does this occur. Repeat the procedure and of course, take 
copious quantities of notes as to what  distance it happens, time of day 
etc. Repeat the whole procedure at different times of the day and night 
and for different lights, wall mounted, ceiling mounted, outside lamps, 
street lamps, different houses etc. When you are satisfied that your 
children can apparently turn lights on without touching them call in an 
electrical engineer and make sure the electrics are not faulty. Only if 
all lights (that are off) are turned on by your childrens proximity, 
regardless of time or day, weather conditions, time of year, type of light 
and all possible errors, mistakes and faults would a scientist be happy a 
new phenomena has been discovered. 

In any experiment designed to investigate a possible new effect it is 
necessary to be absolutely (as far as possible) sure that all possible 
causes are accounted for and ruled out. It is then necessary to get some 
one else to do the same experiment and get the same results. This is why 
science is 99.99% pure tedium, doing the same thing again and again to 
make sure no mistakes are made. The 0.001% of the time something 
interesting happens makes it worthwhile. 

When you have done all the above and are happy a new phenomena has been 
discovered I would suggest contacting your local University's Science 
department and have them double check everything. Another person to 
contact is James Randi, a professional skeptic, who has offered large 
money prizes to anyone who can provide undeniable evidence for the 
paranormal. 

Apologies if this sounds like a harsh and supercritical answer to your 
question but you will find that scientists are very demanding as to what 
proof is required before they tentatively publish a new finding. If a 
mistake is made then it is guaranteed some one some where will find it and 
refute you. If nothing else you look foolish, at worse your reputation is 
damaged.