Animal Welfare Professionals

This is hands down my suggestion for anyone with pets.  Play music FOR  them.  I volunteer with the local shelter and the local rescue.  I am the "Music Man" bringing in my CD Player/Radio and playing classical music and movie soundtrack:  instrumental particularly and acoustic guitar prominent. This I have found works wonders in relieving stress while cats are waiting for adoptions.  It also helps them adjust to their environment and have a sense of something outside their confines, and perhaps reconnect with something good in their previous homes.  I have observed them closely individually and there is practically no cats who aren't affected positively.  It doesn't require much money.  I have had donations of CD players and found good used ones at the local thrift store very cheap.  Give your pet the gift of music every day.  It will enrich their lives even when you aren't there. Love.

Great idea, Steve! I'm off to find a radio!

I agree with Steve  M.  Studies have been done on the positive results for dogs when they listen to music.  I don't know about cat's with this though.

I used to volunteer at a no kill shelter.  Different dogs depending on their age, health, and personality determined what I would do with them.  One dog in particular who had long fur enjoyed a good brushing, and I'm sure the special attention that went with that.  She even liked when I bathed her.

More active dogs enjoyed a good game of fetch, and I took the time to teach, sit, stay and come in the game.

We also play music for cats, we rotate that with TV's showing videos of birds and mice.  My favorite enrichment though is using birds songs (youtube) combined with waving feather wands.  Every cat in the shelter wakes up and engages.  It is really fun.

Enrichment!! One of my favorite topics.
I'm a behavior specialist at a shelter, so I try to get creative with enrichment as much as possible. We love to do snuffle parks and shreddable snuffle boxes as well as snuffle mats.
We also love to do "confidence courses" which include all kinds of novel items for the dogs to explore, like tunnels, skateboards, baskets of laundry, gates laid out on the floor (we love throwing treats in the crevices to encourage them to climb across the surface and investigate!), etc..
For our diggers, I like to fill a baby pool with towels (some have scent, some don't), so they can dig and bury their bones and whatnot.
Cats! We love puzzle treat toys (you can feed them in an egg carton so they have to work for it a bit, or bat the food out...same with boxes that have different sized toilet paper tubes...great for treat puzzles!), and different textured surfaces (bathmats and rugs, pillows, sometimes crunchy paper or bubble wrap). We do clicker training with some of the cats too. Bubbles are great for the active ones, and many of our volunteers like to sit and read with the more reserved ones. We also make toy mobiles when we have time, with jingle balls and stringy things dangling off of them.