Are there any DNA base sequences that are fully conserved between the genomes of all humans?
In 2004 Bejerano et al. identified "481 segments longer than 200 base pairs (bp) that are absolutely conserved (100% identity with no insertions or deletions) between orthologous regions of the human, rat, and mouse genomes". These were found to be mostly in/around genes related to RNA processing, which is perhaps unsurprising given that it is such a primitive/inherent biological process.

Bejerano's paper has been cited over 500 times on Scopus, with numerous papers reporting variants in such regions that cause diseases such as colorectal adenocarcinomas.



So few conserved regions exist because there is plenty of redundancy in the genome; many genes functionally overlap with others, and many genetic variants are 'silent' - they have no effect on the phenotype. Having this variability is advantageous in Darwinian terms because this increases the evolvability of the species.

There are many regions of very high homology between individuals (protein-coding regions are highly conserved even between species), but there will still be natural variation; each mutations effect will be dependent on the rest of the genome. Genes work together to produce a working organism - they do not each code for a little 'bit', and therefore a change in one portion of the DNA may be 'balanced' by a change elsewhere. 

It is only in 'ultra-conserved' sequences that mutations are presumably incompatible with life because the process is so finely-tuned and indispensable.