Many times when a spouse passes, the surviving spouse will purchase a double or companion monument.  This means that the headstone, footstone, or anything else that is being used to mark the grave, is now centered over 2 graves as opposed to just one.  This kind of monument arrangement offers significant benefits over going with a conventional single monument at the time, and then matching another single later on:

To begin with, most people are concerned about cost, and even though the monument is bigger and costs more than a single monument upfront, in the long term it turns out to be cost-effective.  Whether granite or bronze, companion monuments require more material than a single monument.  When the surviving spouse passes though, the only thing left to do is engrave the empty side of the monument, which is a lot less expensive than purchasing a brand new monument.  Materials also fluctuate in cost, and knowing that engraving is the only future task to complete will leave you with financial piece of mind.

Secondly, just as couples like to be buried side by side, it is also preferred by many to share a joint monument.  The feelings of love and unity remain visible to all even after both individuals have passed.   Companion monuments leave room for separate inscriptions and emblems, while maintaining a look of togetherness.  Sometimes double monuments can be made of one piece of material, or separate pieces combined.  Either way the effect is achieved.

Lastly, because companion monuments are generally larger than individual ones, the family name on the stone will usually be accented.  A large visual of the family name makes it easier for cemetery visitors to find their loved ones, instead of scavenging around the cemetery.  In the event that more than two graves are owned at the location, a larger family name will create a general consensus that the area is occupied by that specific family.

Even though all of these benefits exist, some people still prefer to have their own single monuments, which is just as fine.  Remember, these monuments are up for you and your family members to be able to visit and remember your loved ones, so make arrangements based on your preferences.