Bang in a can. Bring one to UFO parties. Remember to run once lit.
The usual tactic is to set the timer, drop them on the ground, run away. However, they can be thrown a useful distance by a strong soldier, becoming good for general purpose throwing at 40 or more strength. High Explosives remain relevant all game long as they are stronger than alien grenades, capable of killing most enemies and terror units in one explosion.
Another tactic is to give the high explosive to a rookie with low stats, go into a small UFO or structure, and set the timer at 0. Be careful sacrificing rookies around UFO Power Sources as this may destroy precious Elerium!
Bug: Dropping the high explosive rather than throwing it will often not attribute any hit experience to the person dropping the explosive if it hurts enemies in the blast. This is because the game will not assign ownership of the explosive to the right soldier until it is thrown.
To work around this bug, you must throw the explosive, during or well before its intended use. The explosive remembers the last person who threw it, and will award any experience to that person. This applies to all other grenades as well, with the exception of the proximity mine.
Tip: If set next to a UFO's diagonal wall, the explosion will go into the UFO and detonate navigation consoles on the far side. Roast 'em in the shell.
Tip: For strong characters who want to throw these things like grenades... be aware you can set the timer and as long as they are not on the ground, they won't explode. So you can prime them this turn, then throw them on a later turn, giving you much more movement TU.
OpenXCOM improves throwing arcs and allows grenades to be primed in the deployment menu, opening up new life for grenade lovers. Load up a "grenadier" with multiple primed Hi-Ex to create a demolition powerhouse, capable of marking multiple targets for certain death in a single turn. Do note that as per XCOM destruction rules, grenades will harmlessly destroy other grenades in their blast radius. This limits the ability to stack explosives against Mutons and Sectopods, who are most likely to survive.