I'm not talking about eating tofu, but the expression that means something more like taking advantage of someone. What exactly does 吃豆腐 mean, and where does this expression come from?
I've only heard it used in describing sexual situations, and wiktionary.org describes its usage as follows:
This idiom usually only refers to a man taking advantage of a woman in a sexual situation.
A typical example would be some creepy guy pinching the flight attendant's backside as she walks past.
There's also a good discussion at wordreference.com.
不要吃我豆腐 is telling someone not to take advantage of me, but specifically in a sexual way, as in inappropriate touches etc. However, the accusation is not very serious in Chinese, and sometimes said in a joking manner. I would translate it as "Don't harasse me!", "Get your hands off me!" etc., but understand that the Chinese expression is softer.
I found an origin story on chinese-forums.com, but I'm not sure how reliable it is.
It’s said that tofu shops usually were run by wife and husband in the old days. Female boss in a tofu shop took tofu as their daily food, which made their skin tender and smooth. On one hand their fine skin helped attract more customers, on the other hand it showed some kind of coquetry to them. Men liked to take “to eat tofu” as an excuse to go to a tofu shop and flirt with the female boss there, verbally or even physically. Therefore, wives, feeling jealous, scolded their husbands, “Today, you went to eat tofu again?!” Now, “eating tofu” has become a word to describe man flirts with woman.
吃豆腐 refers to sexual harassment or men being frivolous with women.
Apparently it refers to a Tofu-shop a long time ago where the husbands rubs the tofu at night and the wife sells it during the day. To sell more tofu the wife flirts with her customers and the customers even grope her. The jealous wives of these "customers" will afterwards complain to their husbands: "So you went out to eat tofu again"
Edit: I can't find the real source of the story, but you can find it on many Chinese sites. It's probably a tale. About the translation, there are many possible gradations. I can go from "I (will) take advantage of you" to "I'll molest you" (actually it can both be in the past, the present or the future). Sometimes 吃豆腐 can also mean to crack a joke, but it's not the most common translation.
There's a section about the history of the term 「吃豆腐」on Wikipedia. I have translated some of it.
「吃豆腐」can have two meanings:
take advantage of somebody
In Jiangsu and Zhejiang, there's a tradition to treat family members and neighbors who have helped in the funeral with thick tofu soup. Some people goofing around will come over for a meal as if they've helped.
take advantage of somebody sexually (this usage is more common nowadays.)
About the same as Don Kirkby♦'s answer.
You are all experts on chinese culcure. But allow me to add some comment. Another Chineses expression regarding 吃我豆腐 is 占我便宜,which also means taking advantage of me. But in the contemporary era, girls use 吃我豆腐 to expecially describe some one touched her boobs. Because they bear great similarities in both appearance and feel.