Yes, in most cases you can mix breeds of chickens in your flock. They generally get on very well. You can even include both bantam and large fowl breeds in your flock, if that is what you prefer. In fact, bantams don't always or even usually end up on the lower end of the pecking order just because they're smaller.
Pro Tip: When mixing different bird sizes, you will simply need to make certain that you have your feeders and waterers set at a height so that all your chickens can easily reach them.
Problems can occur "mixing" breeds in a flock when you have, say, six chickens that are very similar looking (like Rhode Island Reds and New Hampshire Reds) and then one chicken who is of a very different type, like a Polish or a Faverolles. Chickens who look entirely different from the rest of your flock can get picked on (often the other chickens will pick at the large crest of the Polish, or the beard or feathered legs of the Faverolles.) We think their birdy-brains are telling them they're being a great help in trying to clean off that mop of feathers that is stuck where they think feathers shouldn't be! Interestingly, in our experience, Silkies usually get on well with other chicken breeds, despite their unusual plumage, presuming you have several (and not just one lone "different" bird).
The most problematic birds to include in a mixed flock are Polish or other crested birds, because large crests sometimes prevent them from seeing the attack coming--and Faverolles, because they can be so submissive that they usually end up at the bottom of the pecking order. However, if you are raising a flock of many chickens that all have different looks, the birds have a sort of broader idea of what a chicken should look like, and don't usually pick on one another. Of course, the more room they have, too, the better they will be. If they can range on pasture every day, they have things to occupy their thoughts other than why Bessie is wearing that silly and unusual plumage!