The shopping cart is used by two rabbids in Rabbids Go Home. It was used to collect (or steal) all the stuff the rabbids were planning to use for their pile to reach the moon.
If the game is left idle on the start up screen, one of the video that plays shows how the two Rabbids discovered the shopping cart in a parking lot. One of the Rabbids, ends up inside the shopping cart and panics think it is trapped. The other Rabbid ends up in the cart as well and both begin to panic and shake up and down causing the cart to move. Realizing it is moving the Rabbids continue to shake allowing them the move the cart. It is implied that they eventually learn how to exit the cart, and discovered they could use it to travel around. The cart is extremely durable, able to handle repeated abuse the Rabbids put it through, such as using it to dislodge a jet engine from an airplane or ramming it into objects and people. It also appears to have a near infinite capacity for holding and carrying a lot of stuff, regardless of the size, mass, or weight (to the point of defying the laws of physics). It also apparently light enough to be used as improvised watercraft or glide through the air providing they are carrying Barney's Bubble Bed. Turning the cart sharply will cause its tires to spark which somehow allows the cart to preform a speed boost (however it is implied that Rabbids can preform this technique without the aid of the cart as one of the Painter Rabbids did when they where explaining how to due it, the Painter Rabbid was able to produce sparks and boost, even without a cart of its own).
In the TV series, Rabbids sometimes ride inside Shopping carts, usually when they are playing around in supermarkets.