I've heard about The Tale of Genji, and thought I might like to read it. However, there are a daunting number of translations available! They're enumerated in the Wikipedia article.
Here's my rough summary:
0) Murasaki Shikibu - the original Japanese author.
1) Kencho Suematsu - first translation, considered poor quality.
2) Arthur Waley - many errors and changes from Murasaki's original.
3) Edward G. Seidensticker - closer to the original than Waley, but still makes changes.
4) Royall Tyler - more footnoting explaining cultural aspects.
In the end, I think I'm going for either the poetic Seidensticker version, or Waley's more complex writing.