Is it appropriate to make jokes?

And when is it?
I am not talking about inappropriate/borderline jokes that you wouldn't want your entourage to tell either at a family gathering or at work.
I am asking about plain and silly jokes.
I am often tempted to make a funny comment regarding a situation, conversation or words I consider humorous.
Some people see jokes as inappropriate in a professional environments, while others see it as an ice breaker and bonding element.

No later than yesterday night, I was in a situation where I had to bite my tongue to avoid a joke. I was at a social event and met a translator and interpreter Japanese/Singlish. After she introduced herself, I asked her in she was working for a certain industry or is she had any areas of predilection. She explained to me as a translator she works for any kind of company and products or services. As an interpreter, she usually works for conferences or official visits. Then she added that she is working at lot a the zoo. Here, a 1000 thought came to my mind - come on, an interpreter at the zoo! I didn't dare saying anything though and she explained the reason of her work over there. Grown up conversation.
However, two minutes later, she told me that she drank to much the previous day and at this event, it was a third glass and she was starting to feel tipsy. I guess my comments would not have been weird.
So I wasn't able to read the situation correctly enough to feel at ease with a funny comment.
On the other hand, when you do make a funny comment and nobody answers to it, it feel really uncomfortable. So we learn to be serious and take things seriously. 
Is it the way to connect? work? or don't we need to relax and enjoy a good laugh, sometimes?