Laying new plywood or osb over top of existing subfloor?

when the old is seriously damaged [rot, heavy mold, etc.] I'd be inclined to pull it up so I can repair the supports before putting down new

you really need to assess the condition of the old sub floor... laying new wood on top of damp is never a good idea... if the sub floor is damp then you should need to lay a damp proof membrane between the old and the new .

AS others have said, repair rotten or warped floor boards before putting down new subfloor. I'll add two things:

1) Stagger your new boards so they don't overlap the old ones. In other words, the seams of old and new boards should be offset, not on top of each other.

2) Transitions. Are you changing the level of the ENTIRE floor or just one section? If just one section, then think now about how you will transition the level of the new floor into an older section of floor.

Repair and replace and damage, rot and such first. You also may wish to consider the age of the house and how it was built before adding that extra weight.

It is only worth doing if you are going to tile the floor, or use thin sheet materials like vinyl that may reveal the joints in floorboards. Unless your floor boarding is very cupped, or ridged, 1/8th inch ply, or hardboard is usually fine. Remember to condition hardboards before laying. If you have plain edge boarding it is often recommended to improve fire protection. If carpeting it is a lot of additional expense and weight that is not required and you would simply use an underlay on paper if the floor is in good condition. Bear in mind if you have a lot of services that may need access, it will be inconvenient if you want to lift boards, but that is not usually a consideration in a domestic property. Adding a lot of height can lead to problems at doorways.

As long as the old floor is solid, straight and level, with no rotton wood, you should be good to go. Good luck.