Bdelloid rotifers have survived 80 million years with no sex at all; no male of the species has ever been observed. And while they don't seem to be sharing genes with each other, they are definitely getting some on the side--from other organisms.
The rotifers act like genetic vacuums, scooping up genes around with abandon and putting them to use in their own bodies. The ones that help the rotifer survive are kept around in the population--some perform useful functions, like breaking certain chemical bonds--while those that don't help die off. To keep them around, the rotifers stitch these genes onto the ends of their genomes and pass them along to their genetically identical offspring. The variety with the best combination of genes wins the evolutionary race.
Some rotifers seemed to have developed an alternate strategy for evading parasites: Instead of evolving alongside them, forever developing new countermeasures, they beat them in a test of endurance. Rotifers are able to survive extremely hostile environments by slipping into a dehydrated dormant state. When the environment becomes more favorable, they rehydrate and spring alive again (sometimes months or years later), freed from infectious agents that don't have the rotifer's toughness.