As for clover. most of them are weeds. Well, either that or they're used as forage plants for animals. They also make great honey, but they sure aren't houseplants. The most common clover and the most accessible is Dutch White Clover which makes a great lawn-replacement. I, for one, want to try using this clover for parts of my lawn. It's resilient to the point that it can often kill off other weeds. It's short so you don't need to cut it as much. And it helps feed wildlife, whether you like it or not.
Another plant often confused with clover and called Shamrock is the Oxalis. Oxalis is a very large family of plants and it's sold as perennial wood-sorrel. It can also be found as an indoor plant in some area. In the spring you can often get it as a bulbs for spring planting, or you can just wait for the spring and summer season to get is as a plant. As an indoor plant, you don't find it too often. The problem with Oxalis as an indoor plant is it's limited life-span on the shelf. As a green plant, it's only really of interest to people around St. Patrick's day. That makes this plant considerably less valuable to growers. A newer variety called Copper Glow is a nice yellow and red colour with small yellow flowers and works very well as an indoor plant. It's a little more common, though not really suited to St. Patrick's day.
In warmer climates, you can sometimes find green shamrocks or you can grow your own lawn of shamrocks, but in colder areas, you're limited to non-green shamrocks, or grow your own bulbs indoor. And, as always, keep searching for that elusive four-leaf clover in the spring!