How are all life forms connected? Are they linked by one giant family tree, a web, or a forest of family trees? Here I propose to use taxonomically restricted essential genes and essential non-coding DNA elements to determine whether two organisms can be two branches of the same family tree, or can share a common ancestor that is simpler than the two organisms, based on the following reasons: 1) All essential genes and essential non-coding DNA elements of an organism are indispensible for its survival. 2) Spontaneous mutation accumulation experiments show that experimentally-identified spontaneous mutations are mostly single base substitutions, small (<13 base pairs) indels, and rearrangements of DNA segments. No novel genes have been observed to emerge. 3) Targeted mutagenesis experiments show that functional arrangements of amino acids are extremely rare; one in 1077 for a typical protein domain with 153 amino acids. 4) Both mutation accumulation experiments and studies of symbiotic organisms show that genes that are not used tend to be degenerated or totally deleted. 5) For each constructive path to a new functional gene, there are many disruptive sidetracks. These sidetracks may prevent the cells from taking a constructive path that is of no immediate use, however beneficial it might be theoretically. In essence, the very nature of the essential genes and of the essential non-coding DNA elements of an organism, and the inability of mutation and natural selection to create novel genes, argue that two taxa, each with its own taxonomically restricted essential genes and essential noncoding DNA elements, cannot have shared and evolved from a simpler common ancestor. Analyses of the taxonomic distribution of essential genes and essential non-coding DNA elements of six bacteria and five eukaryotes show that no two of them can belong to the same family tree, which indicates that life forms on earth are best represented as a forest of family trees.