What's the best way to increase the range of my 802.11g router?

I have cable broadband, and as such the router has to be attached to a cable modem which also has to connect to the TV. That means the router is stuck in the corner of my house.

This is good when I'm in the street at the front of the house, but not in my bedroom, kitchen or garden.

Without moving my bed into the street, what's the best way to increase the range of the router? I primarily use it with devices such as an iPod Touch which isn't 802.11n capable, so that's not really a solution.

The best way is to buy an extender [repeater], but those are expensive.
Buying a better antenna (if you have a weak one) is slightly cheaper and can help as well.
But not all routers make it easy to change the antenna, in some cases they glue it in even though it's connected as a screw-attachment.

Other than that, trying to optimise the location of the router might help.
High and in the center of the area is usually good.
Some antennas come with an extended cable so you can locate them in a better place even if the router is wall-bound.

There is this really good article on increasing the range of Wi-Fi networks. O are:

2. Move the router off the floor and keep it as far as possible from walls and metal objects. As we mentioned earlier, metal, walls and floors wreak havoc with your router's wireless signal. The more of these obstacles your router needs to punch through to reach your notebook, the worse the interference, and the slower your connection will be.

3. Place your router (or access point) in a central location in the office. If your wireless router is at one end of the office (or your home), the signal will have farther to go to reach the other end. Using a central spot splits the difference.

4. Upgrade your router's antenna. Most routers come with an omni-directional antenna --meaning that it broadcasts and receives in all directions with equal efficiency. If you don't know where your receiving notebooks will be, or if they are indeed scattered in a random 360-degree pattern, omni-directional is fine. However, if (as is most often the case) your router is near an outside wall, with most of the network computers in a 180-degree pattern in one direction only (that is, toward the opposite outside wall), you are wasting half of the router's signal. If you upgrade to a hi-gain directional antenna that focuses the wireless signals in only one direction, you can maximize the efficiency of the system by aiming the signal in the direction you need it.

6. Check your wireless channel, and change it if necessary. Wireless routers use one of 11 possible channels to broadcast. If another wireless network nearby happens to be broadcasting on the same channel your router is using, both networks will experience severe loss of range and power. You can use the wireless software on your notebook to find out how many wireless networks are active in the area, and which channels each is using. If you discover that another network is using the same channel as your router, log into the router via your browser and use its built-in configuration screen to select an unused channel. Chances are your signal strength will improve significantly. (You don't need to adjust your notebook; it's designed to automatically detect the network's new channel.)