It looks like it could be a species of Kalanchoe.There are quite a few species of this with various different forms and flowers, but all are in the Crassulaceae family, which typically have fleshy leaves (not all do) and are typically succulent to semi-succulent. Your plant is quite beautiful. You may be able to easily root larger leaves taken at the nodes.
K. blossfeldiana. A staple of supermarket floral departments and similar venues, like many florist pot crops not necessarily intended to be kept and grown on by the consumer but rather tossed like a spent cut bouquet - ordinary room interiors are often too dim for this particular plant to grow normally. In fact, a need for much higher light levels than foliage house plants will tolerate is true of flowering house plants in general - a very forgiving exception is the variously colored Schlumbergera cacti that are much sold during the holiday season.
