Cherwell
Just about the best known and most popular, this is a newspaper in format and comes out weekly. It has won loads of awards and is certainly worth getting involved in if you want something good for your CV. More real than...
Oxford Student
Again a newspaper, but it is less popular and is published by the SU. Tabloid format with some decent writing, watched by the broadsheets so good to be involved with if you want to go further in journalism.
The Word
This is still a newspaper but tackles more meaty subjects. Articles are generally features. There is a more significant arts influence as well.
Isis
A magazine this time. Quite pretty, fairly well read and with a huge tradition that pulls in top interviewees.
Phoenix
This is really just a platform for student expression. It collects the best in poetry and prose. The standard is very high, but it should be at Oxford! It comes out once a term.
The Owl
Criticises all the rest for being dumbed down and maintains an aloof and academic style and thus a low readership.
There are also loads of publications that come from individual colleges. These change quite regularly. Some are quite large and deal with current affairs in well written articles, others are just crap and good only for paper plane making. You can find out a bit about them by reading the individual college guides.