Do you get given your own IP address on dialup?
I am trying to test remote connections from outside my LAN. Will I be given an IP address that I can use for remote desktop and assistance?
Yes, of course you get an IP address on dialup. Otherwise, you would not be able to send or receive any data :-).
What you are probably asking is if you get a "public" IP address (i.e., one not subject to NAT). This depends on the provider, but most will give you a public IP address. However, the address will most likely be different for each dial-in (a so-called "dynamic address"). This makes it a bit inconvenient to use for remoted desktop etc. . See Pulse's answer for ways around this.
Another thing to keep in mind is that the address migtht be firewalled, so not all kind of incoming (or even outgoing) connections are possible. Again, this depends on your provider, so you can only try it.
Dial-up is, as far as I know, nearly always dynamic IP. You can work around the situation of not having a fixed IP address by using DynDNS
Every dial up user will have a dynamic (Always changing at every connection) ip address, the only workaround is DynDns, i'm pretty sure that ISP's can't give out static ip addresses to dial up connections, as every time you connect to the internet on one.. it has to re connect.
ADSL/Cable/ADSL2 Connections are nearly always on, therefor its possible to have a static ip!
Yes, there are some websites which will tell you your IP (in case of NAT, when you are behind a modem, the IP of the modem). GetMyIP.com seems a save choice, contrary to MonaMyIP.com which is totally inappropriate and definitely not SFW.
If you want a static IP address without the need to open a browser on the other machine use services similar to DynDNS as suggested in other answers.