"Twirly" laces that are elasticized laces coiled into a tight helix. The twirly laces can simply be pulled tight [1]. When made for children, they come in a large variety of colours and textures.
The small plastic sheath on the end of shoelaces that keeps the twine from unraveling is called an aglet.
There are many shoelace accessories. There are hooks to help lace shoelaces tightly. They are especially useful for skates where tight lacing is important. Shoelace covers[1] protect the laces, especially in wrestling. Shoelace charms[1] are decorative. Likewise coloured shoelaces. Some dress codes (e.g. high schools) will specifically exclude colour laces and charms. Lacelocks[1] eliminate the need for tieing the laces and hold them together. Laces can be coated to increase friction to help laces stay tied[1].
Using standard shoes and standard shoelaces, a process patent was granted for lacing in a double-helix pattern "resulting in reduced friction and faster and easier tightening and loosening"[1]. Another process patent was issued for an alternative way of tieing shoelaces[1].