Do Macs NEED to use 192.168.0.x IP addresses?

I've always had problems connecting to home networks when the non-Apple ADSL modem/routers I've had over the years self-assign IP addresses outside the 192.168.0.xxx range.

Do Macs need to use said range?
If so, how do you easily configure your non-Apple hardware to STAY in said range? Apart from rebooting and rebooting till an IP address in that range appears and sticks AUTOMATICALLY?

I've never found any easy answer, apart from rebooting both the modem/router and my Mac.

I now have a new wifi modem/router from my ADSL provider, which uses a smart card, mainly in order to be able to use their supplied cordless phone for VoIP. I set it all up, minus the Voip phone, according to their instructions for Macs, and it all seemed to be working: all the right LEDs, the Airport signal on my Macbook was strong, the network appeared under Network preferences, it said I was connected to the internet thru Airport, etc.
But when I tried to go on the web via Safari (and Firefox), I always got a "You're not connected" message.
Network diagnostics solved nothing.
I rebooted the modem/router a few times, and rebooted my Mac, but the IP address under DHCP always stayed in the 192.168.1.xxx range.

The modem/router came set for that range from the factory. I access its config page at 192.168.1.xxx.

Do I have to change that default IP address for the modem/router?
If so, do I have to do it hard-wired via Ethernet?
Or can I use the 192.168.1.xxx range on the Mac?

Any help much appreciated.

the 192.168 is a non-internet routable ip addy. to change that you have to log in to your router and change the ip addy of the router.

You can use any of the non Internet IP routable address blocks on a Mac (10.0.x.x, 172.16.x.x or 198.168.x.x). You need to have the router set to assign IP addresses in one of those ranges via DHCP/NAT and have the Mac set to use DHCP to get an address from the router. Pretty much any commercial router will allow you to set this up manually. By using DHCP you don't have to assign an IP to every computer, the router does it for you as they log on.