Recombination is the method by which organisms can randomly assort their genotypes amongst each other to create offspring with a different haplotype than either of its parents. This can be done by either copying sequences from one homologous chromosome to another (no physical exchange) or crossing over (physical exchange.
Crossing over is a mechanism in eukaryotes by which recombination can occur, in which the two homologous chromosomes contributed by both parents literally cross over and break at certain points to exchange certain sections of the chromosomes amongst each together.
Self fertilizing organisms typically do not produce offspring that are genetically identical. However, this has an inbreeding effect on its offspring, since it is recombining from the same genotype and so has a higher chance of producing homozygous offspring. This is very detrimental for mammals and some eukaryotes, but in some other organisms such as bacteria, homozygosity is typically not an issue.