What coins have notched edges?

The actual term is "reeded" rather than "notched". Reeded edges were once used to prevent thieves from clipping coins, that is, shaving metal from the edges where it wouldn't be noticed.

If you're referring to US Coins, all former silver and gold coins had reeded edges to prevent clipping of those precious metals.

Today dimes, quarters, and half dollars are reeded simply because their designs haven't been significantly changed since the days they were made of silver. The brass $1 coins introduced in 2000 are a new size and design, and have smooth edges to help differentiate them from the other denominations.

Many countries now use variations of standard reeding to help make their coins distinguishable by touch as well as sight, especially if they're similar in size. For example some euro coins have wide reeding, others have very narrow reeding, and still others have what's called "interrupted" reeding with interspersed smooth spaces.