Christianity claims to be monotheistic (as do the other Abrahamic religions). It's right there in the first commandment. But if it weren't for the Christians' own insistence on this term, would people really label Christianity as monotheistic?
I'll ignore the trinity for this discussion. The father son relationship would certainly seem to suggest at least two deities, but let's just accept the Christian explanation, and assume that they're different manifestations of the same god.
Let's start off looking at the Catholic saints. There are patron saints for everything, from various illnesses, to occupations, to places. I remember when my wife and I were selling our house, my sister in law suggested we bury a statue of Saint Joseph in our front yard. These characters are deities in all but name.
But not all sects of Christianity accept the saints, so let's move on to another character from Christianity - Satan. Here's a being so powerful that he was able to fight a war against Yahweh. He has his own kingdom, Hell. And many sects of Christianity believe that he's powerful enough to influence events in the universe, and that he's going to wage another war against Yahweh at some point in the future.
Most Christians also believe in angels and demons. Archangels are even mentioned by name in the Bible and other religious texts, such as Michael, Gabriel, Luke, Raphael, Uriel, Metatron, and Azrael. Many Christians also accept the concept of guardian angels. So, while the angels may not be as powerful Yahweh, they do have powers that they can use to influence the world.
Now consider the Greek pantheon. Gaia was the first deity, from whom all the other gods came. After the war between the Olympian Gods and the Titans, there were only three main gods who shared control of the universe - Zeus, Poseidon, and Hades. Yes, there were other lesser gods, but they all answered to those three. It seems like this is fairly comparable to Christianity. There are two primary gods, Yahweh and Satan, and all the lesser gods answer to them. The biggest difference seems to be that Yahweh isn't just a powerful god, he's also the creator god. But other polytheistic religions also have the creator god as the most powerful one (such as Vishnu's role in Hinduism).
Considering all this, it seems that calling Christianity a monotheistic religion is mostly an issue of semantics.