The most famous feline goddess was, of course, Bast, sometimes known as Bastet (although the latter name is apparently redundant, using two feminine endings). There were other gods with feline features, however, the earliest known one being the cheetah-headed Mafdet. The leonine Maahes and
Sekhmet were also part of the Egyptian pantheon at various times, and the former was sometimes seen as Bast's son. Bast herself appears to have been originally portrayed as a lion herself, but was later altered to resemble a domesticated cat, and was sometimes represented as a cat-headed human woman.
Bast was originally associated with the Sun, but the Greeks who settled in Egypt after Alexander the Great's conquest came to associate her with Artemis and the Moon. I've seen it suggested that the lunar symbolism came about because of how a cat looks while curled up to sleep, and I've found indications that cats had previously been associated with the Moon in Greek mythology.
Oh, and for people who take the feline worship as a sign that cats are superior to dogs, some canine mummies were found along with the cat ones, and there was at least one god with canine features.
Anubis was god of the dead, probably because jackals are scavengers, and tended to hang around in cemeteries. It's unlikely that dogs were revered in the same way as cats, but they were still important.