Summary for the TL:DR people: Zerg have a lot in common with Nature. Here are some examples in the current game. Here are some ideas of future units that have attributes in common with creatures in Nature. Your ideas?
It seems that when Blizzard designed the Zerg, they took a look at Nature for inspiration, particularly from the creepy crawly side of insects and arachnids. You can see that many of the units and abilities the Zerg utilize have counterparts with Nature, and as such they have a terrifying familiarity about them, some of which I will mention a little later on.
For example, here are some things that Nature has which the Zerg also have:
Burrow: This attribute is shared by many creatures alike, but the one that most reminds me most of the Zerg is the Wolf Spider. This creature digs a burrow where it can hide undetected by more powerful enemies, and launch a surprise attack on weaker creatures for food.
Queen: Several types of insects have queens, but the one that reminds me mostly of the Zerg Queen is the Honey bee. The queen Honey bee stays in one portion of the hive for her entire life, and consistently lays eggs and keeps the colony expanding. Her workers tend to her and will throw down their lives instantly to protect her.
Regeneration: Nematodes are some of the most interesting creatures when it comes to regeneration. Like the Roach, if they become extremely damaged, they will regenerate their tissue to recover completely. However, what is amazing about nematodes is that if they are cut in half, the two pieces will regenerate into two new creatures. Scary. If only our Roaches could do that...
Spines: The tarantula grows stiff hairs on its abdomen. When it is attacked or threatened by a larger animal, it will pluck these hairs off with its back legs and fling them in the opponents eye. The Hydralisk is a little more lethal manifestation of this.
Power in Numbers: Army ants demonstrate the true ability of a swarm. Endless numbers of tiny workers can overpower and skeletonize a larger creature in mere minutes. Zerglings, especially with their speed upgrades, show this ability in the game as well.
Metamophosis: Every insect starts as an egg, grows to a larva, enters a pupal stage, and then becomes an adult. Some of the most dramatic changes can be seen in butterflies and moths, as they metamorph from catterpillars to coccoons to adults. Every zerg follows this same pattern: larva->egg->Zerg unit.