The animal that can't feel pain is naked mole rats, fish and invertebrates.
Naked mole rats are rodents that have a genetic mutation which makes the naked mole rats insensitive to certain types of pain.
Fish have been shown in some studies that they don't feel pain, although some studies have also indicated that fish might feel a simpler form of pain sensation.
And invertebrates such as insects, jellyfish, crustaceans etc lack the complex nervous systems that are required for pain perception so they don't feel pain.
Spiders and other insects also don't feel pain when squished like humans and other animals feel pain.
Spiders and other insects have a simple nervous system which is different from that of vertebrates including humans, mammals, birds, reptiles, fish and amphibians.
As a result it suggests that spiders and other insects don't feel pain in the same way as humans and other vertebrates.
Insects have been shown in studies to exhibit avoidance behaviors when they are exposed to noxious stimuli, like electric shocks or heat.
Although it does not indicate pain perception.
Insects have some neurons that may be involved in sensing of noxious stimuli, but insects lack the complex network of nociceptive neurons that are found in vertebrates.
Nociceptive neurons are the specialized nerve cells which detect and also transmit pain signals and so insects don't seem to experience pain as they lack this.
Squishing or squashing of bugs and other insects including spiders is okay and is often a pretty humane way of getting rid of them.
But some spiders and other insects can be harmful and so it's best to get rid of them no matter how human or non humane it is.