Thanks, Jeff. To clarify, there were not parallel runways. It was runway 26, and I was approaching from the south, so I pretty much flew straight into the base leg. There were no prior instructions -- when I was 10 miles out, I was told to report on left base for 26. I had heard the tower instruct planes to fly both right and left-hand patterns for the runway.
When I was ready to report, there were three planes actively talking to the tower. One was departing 26. One was close in, and I actually heard the tower tell that plane that they were number two behind a Cessna on base, which I was pretty sure had to be me (if it wasn't then I was in unintentional formation). The third was approaching, but was further out.
You confirmed my second guess -- I probably should have turned final, especially since I could tell from what the tower told the other plane that he had me in mind for #1 to land. I just wonder if there is a general rule -- if you're cleared to base, can you turn final without permission from the tower? Further questions along the same lines that I didn't have to deal with: if a tower tells you to approach straight in, but doesn't expressly clear you to land, can you land? If I had turned final, but hadn't been cleared to land, what would the right have been to do?