In my experience home routers tend to give out the same IP address to the same MAC address fairly reliably most of the time. I do tell my router to assign fixed IP addresses to my machines "just in case" but certainly on my setup it doesn't seem to be needed.
As to public WiFi etc. that would be a different story. I suspect if you returned within the same 24 hours and the pool wasn't used up you would get your old IP again but I wouldn't count on it.

You can change the lease time on this router...I made it every 30 days it will expire and it only gives out 10 addresses now (easier to find if I cannot do the good ol' ifconfig).

I must admit I haven't the ability to change the lease time on mine and haven't seen it on others but my impression has always been that DHCP servers will tend to serve up the same IP to the same MAC anyhow as long as it is not used.

I got my Raspberry Pi working with my Clear Spot router using dhcp. The Clear router can show me the address it gives the Raspberry Pi. Here's what messes me up with the software. The router is only a wireless G. So to give it a boost to wireless N, I use a bridge repeater. This seems to mimick to Clear addresses but the Clear router won't show these. Is there a way to see the addresses that a bridge repeater assigns?

Not sure this is giving you what you want.

To get the IP address in that case. Same recommendation would be to see if the repeater has a management console which indicates the addresses.

Second recommendation would be to RTM (Read The Manual) if you have it for that repeater. Or Google for one online.

I'm thinking you're never going to get 802.11n performance if the wireless link is only 802.11g capable no matter what you do with this repeater. The slowest point of the whole link is the 802.11g router.

If you're attaching your Pi (that what you're doing?) to this repeater to get an 802.11n link. So that may show the speed between the repeater and the Pi is great, and greater so than 802.11g class rates; however ultimately it's all slowed down to 802.11g rates because that's the best the WIFI network can get you.