Yes, cattle do ruminate.
The first three sections of the cow's digestive tract are considered by some to be stomach compartments, and by others to be enlarged areas of the cow's esophagus. Cattle have four compartments like this at the beginning of their digestive tract, and each serves a different purpose.
The first compartment is known as the rumen. This sac is the biggest of the four, and is very close to the cow's mouth. It holds food that hasn't been chewed and wet completely yet, and if you could see inside it you'd be looking at a pile of mashed-up hay or grain. Cows "chew cud" contentedly for hours at a time. They have to break their food into microscopic pieces, and make it have as much surface area as possible in order to get the nutrients out of the tough plant fibers. In order to do this, they spit up and re-chew all that fibrous plant material again and again. The rumen allows them to regurgitate this stuff without affecting the rest of their digestive process.
The second compartment, the reticulum, is commonly called tripe. Its purpose is to begin allowing bacteria in the cow's digestive tract to ferment the fibers, and break them down further. It looks like a white honeycomb, and tastes delicious in pepperpot soup.
The third "stomach" is called the omasum. This looks a bit like nubbly, folded fabric on the inside. It absorbs some more nutrients from the fibrous food, and adds some enzymes which will begin to go to work at actually digesting the food. Up until this point, the cow has been using its stomach compartments to break the food apart, and get it ready for digestion.
In the last "stomach", the omasum, the cow begins to add acids that will make the food finally ready to be processed by the cow's natural bacterial colonists. These live in the cow's intestines, and once the food has passed through all four stomachs these organisms can finally get into the fibrous strands of the cow's usual diet and begin to absorb nutrients from it.
Cows often eat dangerous or sharp objects, or cloth. This stuff usually gets caught in the biggest first sac of the stomach, and can build up there until the cow gets sick. The good thing about having so manyy compartments is that it also prevents dangerous objects from progressing further into the digestive tract, where they might be hard to reach and remove.
Having four "stomachs" also allows the cow to live on a almost wholly fibrous diet of grasses. Only ruminants can have such a large body size and still survive by eating this diet, and they have their extra compartments to thank for it.