Your decision will depend on multiple factors. I have listed here some things for you to consider:

• Do you have a first-floor bedroom and bathroom your parent can use?

• Are you prepared for the increased cost of water, fuel, food, etc. that an extra person adds?

• If you have siblings, have you had a frank discussion with all of them regarding every aspect of the arrangement?

• Are you comfortable working out a financial arrangement for your parent to share the additional cost?

• If your parent requires physical care or supervision, how will it be managed? Are you expecting some form of payment?

• If your parent owns a house, what happens to the home if they move in with you?

• Is any remodeling needed in your home to make the situation work?

• Are you able to designate or clear a room, wing or apartment to give your parent personal space?

Now for psycho-social aspects to consider:

• How do you get along with your parent?
• How does your significant other get along with your parent?
• What happens at vacation time?  
• Are you prepared for your home being a destination for family visits to mom and dad?
• Are you able to handle the extra work of having another person in the home?

It is important that you honestly answer the questions listed above, rather than making decisions on the fly.  Ideally, you have the conversations with your parents and spouse long before it is necessary to make any decisions about living arrangements.  Planning is essential because it is a bit like adding another child to your home (someone with increased care needs).
 
If You Are The Parent:

Try to discuss living arrangements long before the need arises, particularly while you are still busy and too healthy to believe that your situation will change in the near future.  If you have multiple children, get them together and share your wishes for your future.  Too often we refuse to recognize the likelihood of needing some assistance in our later years and fail to plan for it.  “That’s the kid’s problem,” some will say or think.  You are not doing your children any favors with that attitude, or yourself, really.  In the back of our minds, many of us hope to simply pass in our sleep at 95 years of age without prior warning or health issues. I realize that may be what we desire, but it is just not likely. In fact, it is experienced by only a small percentage of those who live into the eighth and ninth decade.