Can I bring a spouse along for a conference?

Yes, it is perfectly normal and accepted, at least in all fields I have heard about. Many conferences also allow one to purchase extra tickets for the social program (conference dinner, excursions) for spouses and accompanying persons.

The only possible source of trouble is how to split the hotel bill, since you will (most likely) be sharing a room. Make sure to inquire in advance with the institution that pays for your trip, or at least ask a colleague what the norm is.

One thing to note is that unscheduled time during conferences (meal times, evenings, weekends, days off, etc) is commonly used by participants for networking, social events, informal scientific discussions, one-on-one collaboration, and so on. If you are planning to spend this time with your spouse instead, you may miss out on those opportunities.

I have done this both as the researcher with the spouse, and as the spouse. I have never encountered any problem with it, nor has it been particularly rare (one conference I went to, by virtue of being in Disney World, I suspect featured more people with their family than without).

The one caveat is to make sure your spouse is prepared to be somewhat ignored during the days of the actual conference, as in my experience it's a bad idea to let the desire to go on vacation interfere with the actual purpose of the conference. So, for example, they may be on their own for dinner for a night or two.

When I was the spouse, I usually used this to go to museums and the like I knew my partner would be less interested in.