I've only really heard it with Hugo and Dickens. If it's true, were less known authors paid like that? What were contemporary reasons for this? How much were they paid per line or word?
Authors being paid by the word were generally writing for magazines or periodicals. Some of Dickens' works were first published in serial. The trend really exploded with pulp magazines (super cheap magazines filled with stories etc) during the first half of the 20th century, with many famous writers using this form of work (since it offered regular and reasonably secure pay. Some famous authors who wrote for pulp mags include Lovecraft, L Ron Hubbard, etc. Serialisation was actually quite common for authors as a form of publishing until more recent times and was always a very common way for sci fi and fantasy authors to write.
I do not write fiction, but I and my fellow nonfiction periodical writers continue to be paid by the word. Professional rates range from 50 cents/word to $10/word and upwards for name-brand writers. Many smaller publications and content mills pay less, but it would be tough to make a living on these lower rates. I have heard that current rates paid by genre fiction magazines are in the 10 cents/word range, but I have no first-hand experience.
Being paid by the word remains common practice in publishing industry, especially for short freelance writing intended for magazines. This practice remains especially common in genre fiction, where most of the published material is submitted unsolicited, rather than being explicitly comissioned. For example, Analog, a pedigreed science fiction magazine, has this to say about it's rates:
Analog pays 8-10 cents per word for short stories up to 7,500 words, 8-8.5 cents per word for longer material (Works between 7500 and approximately 10,000 words by authors who make more than 8 cents a word for short stories will receive a flat rate that will be no less than payment would be for a shorter story.), and 6 cents per word for serials. We prefer lengths between 2,000 and 7,000 words for shorts, 10,000-20,000 words for novelettes/novellas, and 40,000-80,000 for serials. Fact articles are paid for at the rate of 9 cents per word. We pay $1 a line for poetry, which should not exceed 40 lines.
So even today, writer of genre fiction can expect to be paid somewhere between $0.06-$0.20 cents per word, depending on venue and length.