Yahoo produces a ton of content. I believe their Finance and Sports sites are #1. Autos is huge. Their news site is big. Their front page gets massive traffic. They have a ton of other sites as well. And this isn't spammy content farming. They really do have a ton of original as well as quality licensed content (e.g. AP stories). They do extremely well in the realm of content, and with audience engagement around that content. Add in Yahoo Mail, Personals, Answers (ugh), etc. They have a lot of very successful sites.
Yahoo Sports is an excellent sports journalism outlet and probably the only serious competitor to the ESPN monopoly. They broke the story on the Miami recruiting scandal, one of the largest NCAA violations in history, after doing extensive in-depth research.
I think yahoo mail. The feature diff between yahoo mail and gmail is not big enough to justify the switching cost for many people (lost archives, old friends and contacts need to be informed of email change)
The yahoo frontpage is still the starting destination for a large number of people. Without trying to draw conclusions about why people just like to use the frontpage as a jumping of place.