Best Prepaid Cell Service For Overseas?

Hello all! I was wondering if anyone here could offer advice as to what kind of cell phone service to use when we get overseas..any particular companies to stay away from or any ones you've had great experience with.

We will be starting in the UK and spending a bit of time there, then traveling through Europe down to Morocco, then back up through Europe and hopping on a train in Russia to China/Mongolia/maybe Japan (not sure yet). So basically, we're looking for a cell service that can allow us to make phone calls through most of those places if not all, for a reasonable price.

Also, my boyfriend is getting a cell phone he can use with his carrier for 3 months over there then switch the SIM card, but my cell phone service does not carry phones with SIM cards. Would it be a good idea to get an unlocked phone while I'm here then activate it there, or buy one when we arrive over there? What did you guys do?

Sorry for the essay, but I am particularly lost on this matter!
Thanks so much ahead of time,
Kat

Please note that this is not a budget travel site but a wilderness trekking forum (American definition of "backpacking"). You will get far better info on a travel site such as Lonely Planet. Many of us have traveled to Europe but not necessarily recently.

OM is right, this is not a travel site. Having said that, get an unlocked phone and buy SIM cards as you go along. Want service in someplace like Mongolia? Get an Iridium Satphone.