Maximum Distance

This depends on the load of the bus and the speed you run at. In typical applications, the length is a few meters (9-12ft). The maximum capacitive load has been specified (see also the electrical Spec's in the I2C FAQ). Another thing to be taken into account is the amount of noise picked up by long cabling. This noise can disturb the signal transmitted over the bus so badly that it becomes unreadable.

The length can be increased significantly by running at a lower clock frequency. One particular application - clocked at about 500Hz - had a bus length of about 100m (300ft). If you are careful in routing your PCB's and use proper cabling (twisted pair and/or shielded cable), you can also gain some length.

If you need to go far at high speed, you can use an active current source instead of a simple pull-up resistor. Philips has a standalone product for this purpose. Using a charge pump also reduces "ghost signals" caused by reflections at the end of the bus lines.
I'd like to extend the I2C bus. Is there something like a repeater for I2C?

Yes indeed this exists. Philips manufactures a special chip to buffer the bi-directional lines of the I2C bus. Typically, this is a current amplifier. It  forces current into the wiring (a couple of mA). That way you can overcome the capacitance of long wiring.

However, you will need this component on both sides of the line. The charge pump in this devices can deliver currents up to 30mA which is way too much for a normal I2C chip to handle. With these buffers you can handle loads up to 2nF. The charge amplifier 'transforms' this load down to a 200pF load which is still acceptable by I2C components.

© Vincent Himpe 2016