Some common words are 先生 or 老公,
Are there any other options that would be more socially appropriate?
老公 is more for casual conversation. e.g. 這是我老公
先生 can be used in a more formal situation. e.g. 這是我先生
In a even more formal situation, you can use 外子. e.g. 這是外子
more socially appropriate? Probably no one can beat "老公" now.
老公 is the most commonly used words in both mandarin and Cantonese, we usually introduce or describe husband using "這是我的老公。".
As 先生 in Cantonese can also means teacher, so the most appropriate is "呢位係我老公。" In formal written language, 丈夫 also means husband but it is not used in spoken language.
（Old Beijing dialect）
－这 我们 家 挣钱的/管事儿的/拿主意的。/这 (孩儿)他爸。(husband)
－这 我们 家 掌柜的/管账的。/这 (孩儿)他妈。(wife)
(for old people, generally above 50 yrs old)
-这 是 我 老伴儿。
我家死鬼 might be an interesting one. Literally it means "my house dead ghost". It is used usually in a teasing way when mentioning "husband" to a close friend.
As the matter of fact, this question, and the Can we call someone X太太 or not? one, has a common answer in mainland China, at least for the past 40~50 years since "New China" -- it's “爱人”. Both “爱人” & “同志”, were commonly used to address people after year 1949 in mainland China.
Unfortunately it has been viciously attacked and jeered by the HK & TW people, now “爱人”/“同志” are mostly abandoned/avoided. I'm not blaming people here. This is only the sad part of the Chinese language history. For example, I myself would avoid the term “太太”，because it has been negatively associated with “官太太”, “姨太太” in mainland China for a very long time (40~50 years after 1949). This is the main reason that we suddenly feel that that there is no proper ways to say husband/wife in China. “老公”，“老婆” maybe a formal way to address people in some area, but in mainland China, especially the norther side, it is widely regarded as “乡下话”, thus only used informally.
“爱人” can be used both formally in the newspaper and casually among friends. I still think “爱人” is a good answer. Some people demean it by saying it means "lover". But I'd say that is a deliberated disgracing, because "lover" has a proper Chinese translation for very very long time -- “情人”. The proper translation of “爱人” is "beloved significant other", a marvelous word that has no western counterpart.