Meiotic parthenogenesis or automixy happens in case of ants. This causes genetic variation but the offsprings are haploid. I don't know of any case where there is fusion of similar gametes to form a diploid cell. It is difficult for two ova to fuse in natural conditions because the vitelline membrane has to be dissolved. 

Experimentally a haploid ES-cell can be fused to ovum to form a progeny. Haploid ES cells undergo diploidization and when injected in blastocyst, can develop properly ([Ref](http://www.ncbi.nlm.nih.gov/pubmed/21900896)). In fact haploid androgenic-ES cell line had been made in [this study](http://www.nature.com/nature/journal/vaop/ncurrent/full/nature11435.html?WT.ec_id=NATURE-20121004) by injecting sperm into an enucleated oocyte. These androgenic-haploid cell lines can be fused to ovum to give rise to viable offsprings. 

Also see [this question](http://biology.stackexchange.com/questions/2853/is-ovum-ovum-fertilization-possible-for-human). *Similar topic*