Meant to address this in my first post:
They do it with every type of light bulb I install.
Small voltage changes affect incandescent lumen output much more than with CFL or LED. It's unlikely that a small voltage change (from say 120V to 105V) would even affect the latter two types.
I've installed two new ground rods outside figuring it was a grounding issue.
The grounding conductor and pathway are only used under fault conditions. Regardless of if the lights flicker or dim/brighten, a 0.000001 ohm pathway to ground (more properly, back to the source) will have the same effect as a 500 ohm pathway or no pathway: none.
I've redone from the service drop to the panel. I called Eversource (utility company) and told them the issue and they installed a new drop. But nothing is helping with the problem. Then grounds and neutrals are all tight and look fine. I've changed all the devices in my house and I still can't fix the issue. No one else around me is having the same issue. :?
If your lights are
dimming for a few seconds, then returning to normal brightness, and there are no other apparent electrical problems, then it's probably due to a high(er) amperage motor load starting inrush current, like an HVAC unit, or even a dryer. Washing machine motors under agitation can produce faint flickering/dimming. See Tom's post #3 (excellent troubleshooting list) for other causes.
If they
flicker, which is what I'd describe as a much more rapid event of varying intensity, then I'd start looking thru the things I listed in post #2. See if there are any seemingly unrelated events which coincide with the flicker.
In one case, I found shutting an interior door caused a bedroom light to flicker. I banged on the wall next to the switch mounted by the door, and was able to reproduce the flicker. I removed the coverplate and switch and the neutral had popped out of the backstabbed connection. The wires were also barely twisted under a wirenut. I re-made all the connections in the box (which were all loose).
In another case, I found a can light with loose connections. The kids jumping around on the 2nd floor produced enough vibration to cause the connection to momentarily make/break, causing a flicker. In still another can light, I found the center prong of a medium/Edison base lamp was barely making contact with the bulb, causing flickering.
Where you start troubleshooting will depend on where the flicker is, and how many lights/circuits are affected.