How many genes do we share with our mother?
There is a distinct difference between the 'genes' that we share, and the genome (the DNA) that the genes are made of.

All humans (excluding genetic disorders) have the same genes, but the same gene in different individuals may have a slightly different DNA sequence, and this may be manifested in the different traits you can observe between people (eye colour, height, etc) or be ’silent’ (have no observable effect).

So you therefore have 100% of the genes that your mother has.

However, as stated in another answer, you inherit the different 'alleles', or versions, of the genes from your parents, and end up with ~50% of the alleles from each parents (but all the genes).

With regard to species differences; many of the genes we inherit have evolved over millions (in fact billions) of years, and thus many of our genes are present in most other organisms (but in very different forms - the DNA). Chimpanzees are our closest relatives in evolutionary terms, and thus their genes are very similar to ours in the genome (~98% the same). But this only applies to the coding regions! Less than 2% of your genome actually codes for genes - the rest is mostly regulatory (not junk, as it used to be called), and this is where the true inter-species variation lies. So whilst we have ~98% homology in the protein-coding regions, this is MUCH less if you count the whole genome.