Adobe make a whole range of products, and you are likely to have at least 3 on your computer - Flash, Shockwave and Reader. They are all free.
If you get a window asking you to update these then it is fine to go ahead.
I had never heard of Adobe Media Player and I have never had that installed. Assuming you already have it installed then it is ok to install updates.
What other Adobe products you have I dont know - I know they had Adobe Air so you may have that.
Generally it is fine to let Adobe download and install all these updates. Some of them may be to fix security holes so it is best to have them installed.
Note: I have seen examples of "fake" downloads of Adobe Flash. Some web sites "pretend" they are going to download Adobe Flash but instead download a virus. The window looks rather amateurish so if you get that cancel it.
If you get the proper Adobe window again just let Adobe go ahead and install the updates.