I'm aware of three such products that emerged earlier this month, all from Asia. These products are so new (and from such small, PR-challenged companies) that there is scant info on them, other than photographs and minimal specs.
The first is the Sysgration mouse phone from Taiwan. It looks a lot like a regular mouse, but flips open to reveal a keypad, from which you might presumably dial numbers.
The most likely-to-reach-your-desktop product in this category is a Sony flip phone mouse called the VN-CX1. Unlike the Sysgration mouse phone, the Sony device has no build-in keypad.
And, finally, the most stealthy mouse phone is called the Skype Travel Mouse from the Taiwanese company Yiyi Electronics. It looks exactly like an ordinary travel mouse, but when someone calls, you simply pick up the mouse and hold it to your head. Speaker and microphone are on the bottom.