I was wondering whether there are any eukaryotes which never have a diploid phase. I can't think of any. Fungi have diploid stages, and I know any sexually reproducing organisms will have at least transient diploid stages (I am not referring to such transient stages- I mean extended diploid stages so I am counting as a 'haploid' organism one that only ever has two sets of chromosomes for a very short time while it undergoes meiosis.)
Update: There are plenty of eukaryotes that occur in haploid stage as the dominant life cycle stage. See metagenesis in cnidarian animals and "alternation of generation" in algae, protists and fungi. ......
I am not referring to such transient stages.- I mean extended diploid stages so I am counting as a 'haploid' organism one that only ever has two sets of chromosomes for a very short time while it undergoes meiosis.
- Yes there exist a vast lot; and such life cycle pattern is called haplontic life cycle (also called haploid lifecycle)
(Table from Google Books, Protozoology by Karl Gottlieb Grell)
Among slime-molds, Dictyostelium shows haploid lifecycle.
Dictyostelium life cycle diagram from Biology- A dynamic Science, by Russell et al (Google Books)
Advanced BIOLOGY, principles and applications, C.J. Clegg and D. G. Mackean, First Edition (1994), John Murray publications.
College Botany, Vol-2, By Gangulee and Kar, New Central Book Agency, Kolkata.
Some apicomplexans such as Plasmodium spp. are haploid during their asexual stages. The organism spends more time (at least in the human host) in the asexual stage than sexual. source
Plasmodium spp. are haploid in both human and mosquito hosts except for a brief stage in the mosquito midgut where two haploid malaria gametes present in the mosquito's blood meal fuse to form a diploid zygote. This zygote immediately undergoes meiosis to generate four haploid cells that continue in the haploid form, reproducing through mitosis, until several thousand are present in a small sac, the oocyst, attached to the gut wall.
To offer a more multicellular look on life: there are many Hymenoptera species that are haploids their whole life. Many Hymenoptera are haplodiploidy meaning that one sex's life cycle starts out as diploid zygotes and the other sex's life cycle starts out as haploids. Many male bees, ants, wasps, and etc start their life as an unfertilized haploid eggs and remain haploid until their death. Of course, these haploid males cannot be made without a diploid female so this example may technically break your rule.