Grab Bar for shower, toilet, doorways with a step, etc.

Be sure they are mounted securely, into a solid backing 

Shower chair 

These come in many styles to use in a shower stall or bathtub

Non-slip shower mat 

Useful for anyone to prevent falls in the tub or shower

Raised toilet seat with handrails

Can be installed for temporary or permanent use with a few simple tools

One-handed sock aid  

There are several styles of these, but they all allow you to put the sock on the device, then lower the device to your feet for donning socks. Can be tricky to do with one hand.

Shoe horn

Long-handled shoe horn 

Button Hook for one handed buttoning. A little tricky to get the hang of. There's a similar tool with a hook for operating zippers.

Suction-based nail clippers 

for one-handed clipping of finger- or toenails

Rocker knife for one-handed cutting 

Jar opener to compensate for weaker grip strength. You can stabilize the jar or bottle between your legs, or in a drawer that you're leaning against.

Reachers are often sent home with people but not as often used. Handy for picking things up off the floor, pulling up pants, reaching items on a shelf or counter, or poking people.

Playing card holder. You can also use a short section of pool noodle with a slit down its length, or a piece of fat pipe insulation.