If one partner in the marriage converts to Judaism, is it customary for the other to follow suite?

I would say it probably depends on the couple and whether it's important for them to be of the same religion, to raise their kids in a particular religion, etc. The particular denomination the convert chose probably also plays a role; Reform and Reconstructionist Judaism tends to look more favorably on interfaith couples than does Conservative Judaism, though many Conservative congregations will still accept a non-Jew as a member. If someone has an Orthodox conversion, I'd say chances are they would want for their spouse to convert too (and Michelle is quite right - I have a hard time imagining an Orthodox rabbi argreeing to perform a conversion for just one spouse).

Probably the most frequent reason for conversion to Judaism is because one plans to marry a Jewish partner. I'd say that it's less common for a couple to convert to Judaism together, though my husband and I both converted before we married (neither of us was Jewish to begin with).

Most (if not all) rabbis will not convert only one half of a married couple. Certainly no responsible one would. Being Jewish is more than just a belief system, it's a way of life and it has a large impact on the lifestyle not only of the person, but of their entire family. Keeping the Sabbath (let alone kosher) is difficult enough to do as it is, without having someone in the house who is not following the same laws. If the couple are planning to have kids, the couple would have to agree to raise the kids Jewish, and if one of the couple has no interest in Judaism, that is less likely to happen, especially if the other parent is new to Judaism and has no Jewish support network in the extended family.

So yes, if a married person was planning to convert, generally they convince their spouse to do so as well. Otherwise they are just opening the door to a lot of potential heartbreak.

Suit, and no. Though God says he wants us "equally burdened" so it may be a real rocky road ahead for them.