Is there discrimination against single people?

Yes, according to a 2007 study -- here's the abstract:

Providing the first empirical evidence of discrimination against singles, participants in multiple experiments favored married couples over various types of singles and failed to recognize such differential treatment as discrimination. In four experiments, undergraduates and rental agents read descriptions of multiple applicants for a rental property and chose one. The applicant pool, varying across experiments, included a married couple and different types of singles. Although the applicants were similar on substantive dimensions, participants consistently chose the married couple over the singles and explicitly stated that the applicants' marital status influenced their choice.

In Experiment 5, participants read examples of housing discrimination against singles and other more recognized stigmatized groups. Participants rated discrimination against singles as more legitimate than discrimination against virtually all of the other groups.

I got that from a blog post called "Are single people unfairly stereotyped?" on the wonderfully informative blog Barking up the Wrong Tree. That post also links to another study, in which people had to rate other people, and themselves, on a variety of metrics ("personality characteristics" and "overall well-being"). Single people were rated by others as worse than "partnered" people on all the metrics, even though single people rated themselves just as highly as partnered people rated themselves. One exception was "satisfaction with relationship status" -- single people were, not surprisingly, less satisfied than partnered people with their relationship status.

Barking up the Wrong Tree adds:

I haven't seen a very definitive book on being single and this one isn't terribly relevant for guys.

Well, there's Singled Out by Bella DePaulo, who's one of the co-authors of the first study. Here's DePaulo having a conversation on the topic with my mom, Ann Althouse: