I have a project with 2 applications ( books and reader ).
Books application has a table with 4 milions of rows with this fields:
book_title = models.Ch
Like many have said, it's a bit premature to split your table up into smaller tables (horizontal partitioning or even sharding). Databases are made to handle tables of this size, so your performance problem is probably somewhere else.
Indexes are the first step, it sounds like you've done this though. 4 million rows should be ok for the db to handle with an index.
Second, check the number of queries you're running. You can do this with something like the django debug toolbar, and you'll often be surprised how many unnecessary queries are being made.
Caching is the next step, use memcached for pages or parts of pages that are unchanged for most users. This is where you will see your biggest performance boost for the little effort required.
If you really, really need to split up the tables, the latest version of django (1.2 alpha) can handle sharding (eg multi-db), and you should be able to hand write a horizontal partitioning solution (postgres offers an in-db way to do this). Please don't use genre to split the tables! pick something that you wont ever, ever change and that you'll always know when making a query. Like author and divide by first letter of the surname or something. This is a lot of effort and has a number of drawbacks for a database which isn't particularly big --- this is why most people here are advising against it!
[edit]
I left out denormalisation! Put common counts, sums etc in the eg author table to prevent joins on common queries. The downside is that you have to maintain it yourself (until django adds a DenormalizedField). I would look at this during development for clear, straightforward cases or after caching has failed you --- but well before sharding or horizontal partitioning.