The zergling is the least durable basic troop unit. This is offset by inexpensive production, and high movement and attack rate. The zergling is useful throughout the game; it may be used for early game rushes, then as support for more powerful units in the late game (eg. ultraling).
Zerglings should be used in swarms. This is especially important as the game progresses and attacks and abilities inflicting splash or AoE damage become more common. Surround and attack individual enemy units with multiple zerglings at once for quick kills.
If a zergling egg hatches after the controlling player is eliminated, one will spawn normally but the other will become blue and neutral.