Mrs. Crump’s Cat by Linda Smith, illustrated by David Roberts.
Mrs. Crump is a rather grumpy, older woman who lives by herself.  But her life changes when a cat insists on entering her house and staying.  She finds herself buying cream for the cat, even though the grocer warns her not to feed it.  And on her walk back home, it somehow seems shorter.  Each day, Mrs. Crump tries to put the cat out, but then something makes her reconsider.  As the days pass, she gets happier and more friendly.  When she puts up the missing cat flyer to see if the cat belongs to anyone, she describes the cat in very unique terms.  No one claims the cat, so Mrs. Crump has very little choice but to happily live with it.
I enjoyed this more than other unwanted cat stories, because the cat does nothing but simply be a cat.  It is not sneaking back in after being thrown out or making a pest of itself.  It simply is there wanting to be fed, happy to be petted, looking for a warm lap.  Recommend this one to cat lovers.  It is a nice length to share with Kindergarteners or first graders in a cat storytime.