Solution 1:

If it is extremely crowded, you can say "packed like sardines in a can" or just "packed like sardines" or "packed." This comes from the way sardines are tightly packed into cans when canned for eating:

photo of sardines packed in a tin

Strictly speaking, some people will object to this usage: both the place and the people in it can be said to be packed, but only the people can strictly be packed like sardines since the sardines are inside the can and the people are inside the crowded place. However, colloquially people will use the phrase in both senses. Also, most people just say packed:

The subway wasn't working so the buses were all packed.

Solution 2:

Packed to the gills

Packed to the rafters

Packed to the gunnels (from gunwales <- gun walls) (originally of a ship)

A popular East Side bar, packed to the gunwales with arch young bankers and ersatz Now girls.

Pressed like olives/grapes

packed together tighter than two coats of paint

Bursting at the seams (the room was...)

As crowded as a beehive

Big and poor and as crowded as a beehive.

And since we are photo-heavy...

beehive

"I would rather sit on a pumpkin and have it all to myself, than be crowded on a velvet cushion." - Henry David Thoreau

Solution 3:

There was no room to swing a cat? We were pressed together like peas in a pod (often used to indicate uniformity, but sometimes literal closeness)? You couldn't fit a knife/cigarette paper between the [contestants]?