Zergling late-game strategies and uses

Solution 1:

The Adrenal Gland upgrade is very powerful, which I believe is only available after a Hive is built.

Against Terran, if you Dark Swarm them with a Defiler their biggest disadvantage (easily killed) is nullified while under the Dark Swarm. This will allow them to get into melee and inflict lots of damage very quickly. Also, because they are so cheap, you can consume the Zerglings with the Defiler for more energy which you can use to throw out more Dark Swarms.

Against Zerg, if your zerg enemy went early mutalisks you could possibly overwhelm them with zerglings. Mutalisks in small numbers aren't very good at killing zerglings.

Solution 2:

Late game you can get a number of uses out of zerglings, especially once they have the adrenal gland upgrade and some attack upgrades. They can still be used to try to get surrounds on enemy armies, but should generally be moved in as a flanking maneuver after your army engages. They are also useful to build if you have minerals to spare but no gas. Might as well have some extra zerglings rather than floating the money.
They are fairly useless against an army with reavers or archons though, so be careful against protoss. Combining them with a defiler's dark swarm can make them particularly effective vs terran.
Another use of them is the dreaded 'crackling drop'. (Zerglings are often referred to as cracklings after they have the adrenal gland upgrade). A drop of 20+ cracklings into the enemy main or an expo can do massive damage to their base very quickly if their army is not nearby to stop it immediately.
And, of course, they can stay a main part of a regular army composition by using mutas and zerglings to abuse their mobility advantage if the game is rather spread out across the map.

Solution 3:

Late-game, zerglings are most commonly used in conjunction with ultralisks. The ultralisks tank the damage (with the armor upgrade), while zerglings (with adrenals) dish it out. The nice thing about ultra-ling is that your upgrades fit both units since they're both melee.

Muta-ling is another popular combination, but it's more mid-game than late. You use the mobility of speedlings + mutalisks to contain your opponent, while you expand across the map, before teching up to higher level units like defilers and ultras.