It all depends. We are all expected to help and serve - one way or another. In reality for those that are older less is generally asked. At the same time - we revere our more senior members and want to learn from their wisdom and life experiences. 
 
Whatever you do will be worked out between the Bishop and you. You will not be asked to do more than you are capable of.

No matter what members (especially new members) can expect a calling to help them "fit it" and get a deeper understanding of the restored Gospel.  
 
Callings are something the Lord bestows to build us and help us serve his design for His Church.  
 
As a senior citizen you can also consider volunteering to serve a mission. You will not be getting up early knocking doors, you will be working in the mission office supporting the young men and women service missions.

The ward in which I belong contains many older singles. The bishop calls those he feels are able to handle callings, and then only into callings he thinks they can handle. Many of them do not hold a calling at all but it varies depending on circumstance. 
 
If you express your thoughts about what type of involvement you want from a calling to your bishop it would probably be appreciated and very helpful to him. We have had some members who are very active in the ward tell the bishop that they do not want callings, and our bishop respects that. Every once in a while he will ask them if they are ready for one. 
 
We also have a retirement home within our stake where there are a lot of LDS members. The stake organizes meetings to actually go to the retirement home. They have their own sacrament service and everything.