30x is generally considered adequate for variant calling from routine whole genome sequencing using standard Illumina technology, which has a reasonable error rate. But this figure (30 reads covering each base) is just the average of a Poisson distribution - according to Illumina 'the data would be expected to fall to 15x or below about 0.2% of the time', so there will always be some poorly covered bases where we can't confidently call variants.
The biology can also make things interesting - e.g. mosaicism and copy number variations can mean that there are interesting variants at low allelic ratios (i.e., much lower than the 50% you'd expect from a heterozygous change). Cancer is a major challenge, partly because the tumour may be mixed (effectively diluted) with normal tissue (e.g. from blood) reducing our ability to detect purely somatic changes confined to the cancer, and also because of heterogeneity (many, even most, somatic mutations are not in every cell of the tumour). Because of this, tumours are routinely sequenced at higher depth than normal 'germline' DNA by the UK 100k genome project (and others).