I made some progress on this after chatting live with Eric from Digi support, and also reading around HOWTOs on the net.
First point is that the XBee 2.5 model is discontinued and no longer supported by Digi, even though it's still pretty widely sold. Eric mentioned that there are some better and more up-to-date models available, I think the 'ZB' line rather than the 'ZNet' is what you want. But I'm not completely clear on that yet (and I have the 2.5 which I wanted to get working).
Next, because the XBee 2.5 and XBee PRO 2.5 are no longer supported, the firmware is not available automatically from the X-CTU program. To get the firmware, you can still download it manually, and then use the 'File' option in the X-CTU download tool to get X-CTU to use the latest firmware. The firmware I needed was on this page: http://www.digi.com/support/productdetl.jsp?pid=3261&osvid=0&s=269&tp=2&tp2=0
Next, you can follow the information in the 'Xbee Configuration guide', see link at http://www.arduino.cc/en/Guide/ArduinoXbeeShield
You have to set up one XBee as 'ZNET 2.5 COMMUNICATOR AT' (the 'home base' xbee) and the other as 'ZNET 2.5 ROUTER/ENDPOINT AT' (the 'remote' xbee). You can assign names (ID) and network IDs (PAN ID) to both XBees using X-CTU.
Using this approach, the serial test worked OK, so it's looking good. According to Eric, what one should really be doing here is upgrading the firmware to the new 'ZB' feature set, for which instructions are here:
http://ftp1.digi.com/support/documentation/upgradingfromznettozb.pdf
I'm entirely sure why one should do that, other than to enable digi to support you better, because they don't actually support the ZNet modules, which apparently date from year 2006.
Recommend you get yourself one of these. It's well worth the price and will save you a lot of headaches. Programming can get complex, if you're doing it manually instead of using X-CTU. Since you really only have to do it once, it's much easier to tweak the settings in X-CTU and not bother with the programming code within your application.
About the only thing you can really do with a single XBee is learn about it: fiddle with the settings and whatnot. When you've learned all you can, you'll have to buy another one. :)
Best Answer
I've "bricked" a series 1 and was able to recover it by a combination of the following. YMMV since you have a different version, but worth a try.
Obvious setting - the port speed. Stick with 9600 till everything works.
If your original firmware is much (much) older than the latest release - try to flash a less newer release from X-CTU first. Then, step up to the latest firmware.
If the XBee is not responding to AT commands. Change your PC (assuming Windows) port settings to use HARDWARE FLOW CONTROL (control panel, device manager, ports, COMx). Unplug and replug the XBee USB explorer. Start X-CTU. Don't try to test the port, just go into MODEM CONFIG tab, leave the firmware option UNCHECKED at first, click the RESTORE button. This should recover the XBee to a factory default. Then step up to an interim (less newer) firmware release and check the ALWAYS UPDATE FIRMWARE box, click WRITE. Do it twice. Then select the latest firmware release. Click WRITE. Uncheck the firmware box. Click WRITE. This should get the XBee alive again. Then you may make config changes as required, just watch that port speed, I've not been able to get my Series 1 higher than 9600 with any level of reliability.