Different species have different numbers of chromosomes---fruit flies have only 4, while there are amoebas that have millions. There is little if any relationship between the complexity of an organism and the number of chromosomes it has. Geneticists are still not entirely sure what decides the number of chromosomes, or how it relates to the evolution of an organism.
In humans in particular, the number is relatively consistent; almost all humans have 22 regular chromosome pairs (autosomes), and 1 extra pair that decides our sex (sex chromosomes).
There are a few rare genetic disorders---most of them serious or even fatal---that involve having one more or one fewer chromosome. Examples include Turner Syndrome, Triple X Syndrome, Patau Syndrome, and Edwards Syndrome. For the worst of these disorders, often fetuses with these syndromes will die before they are even born.