Surely you can use TeamCity without IntelliJ IDEA. You can use TeamCity for Java and .NET projects and get build reports and notifications on the web, standalone Windows tray notifier, E-mail, Jabber/XMPP.
In IntelliJ IDEA you can have really nice integration with interesting TeamCity features like server-side code inspections, code coverage. There is unique remote run feature which is available only using this integration.
We also plan to implement TeamCity plugins for other IDEs, like Visual Studio and Eclipse (basic support for Visual Studio will be available in this year, Eclipse plugin is planned for the first quarter of 2007.