Using full-width grid or tick lines

Use full-width lines with your tick marks when specific numbers are really important.

If your reader only needs to know that A is bigger than B, don't use full-width lines, just use small ticks on the axis. If your reader is going to spend some time with the graphic and be interested that A is 45.65 and B is 37.66, that's when you use full-width lines.

Backgrounding grid or tick lines

If you're using full-width grid/tick lines, you need to make them much less obvious than the dots, bars or lines that are your actual data points. I call this "backgrounding."

The rule boils down to don't make them black lines.

If your background is white(-ish), you should make the lines grey.

You could also make the lines light grey and dotted. Dotted usually looks better than dashed, but there are certainly times when dashed looks good, too.

If your chart's background is grey, you can make your grid lines white so they're kind of using negative space - or a slightly darker grey because obviously everything ever should be grey.