There are several trees that you can grow indoor, but by far the most common (and the easiest to care for) is the Ficus Bonsai. The Ficus is tolerant of low humidity and can withstand quite a lot; a good choice for beginners.
Also known as Banyan Fig and Taiwan Ficus. The Retusa has small, dark green leaves that alternate up the stem and which are more oval than the Benjamina. Grey to reddish bark dotted with small, horizontal flecks, similar to tiger-like markings. All have heavy trunks and all are trained in the traditional curved shape. Among the most tolerant, versatile and trouble-free bonsai trees for indoor use.