A birdbath in the middle of the slab
Every trowel finish leaves the surface within a small tolerance of dead flat, not perfectly flat, and a shallow dip somewhere in the middle of a big patio or driveway is common. Rain collects there, sits for a couple of hours, and dries out once the sun and air get to it, the same as the rest of the slab. It does not grow, it does not move toward the house, and it does not leave a wet line months later. That kind of birdbath is a cosmetic issue, not a structural one, and most slabs have one somewhere if you look after a hard rain.
Pooling at the edge or against the house
Water sitting at the perimeter of a slab, especially where it meets a foundation, a garage door, or a step, is a different situation. Concrete is supposed to be pitched to carry water away from the structure it sits next to, and pooling right there usually means that pitch has gone wrong, either because it was never set correctly to begin with or because part of the slab has settled and tipped the low point toward the house instead of away from it.
A wet spot that used to dry out and now does not
The most telling pattern is a slab that used to shed water fine and has started holding it somewhere new. That points at the subgrade, the ground the slab actually rests on, changing, not the concrete. Red clay swells when it is wet and shrinks when it dries, fill that never got proper compaction settles under years of load, and water running under an edge from a downspout or a bad grade can wash the fines out from under a slab and leave it sitting lower than it was poured, sometimes with a settlement crack marking the low corner. Our page on tear out and replacement goes into what that base failure looks like and what fixing it actually involves.
What the standing water is doing while it sits there
Water sitting on concrete is not just cosmetic once it starts freezing. At this elevation, a puddle that would only be a nuisance somewhere flatter and warmer goes through repeated freeze and thaw cycles over a winter, and that is harder on the surface right under the puddle than on concrete that sheds water and dries. A birdbath that only holds water for an hour or two rarely gets cold enough for long enough to matter. Standing water that lasts overnight in freezing weather is a different story.