Fortunately, the option to link your videos to other videos isn't completely disappearing from YouTube. You will still be able to use "end screens" to link to other videos and playlists within YouTube.
To use the end screen options in YouTube you must first select "end screen" on one your own YouTube uploads. Then you can choose "add element" followed by "video or playlist" to link your first video to a subsequent video. The steps for this process are outlined in my screenshots included below. (Click the images to view them in full size).
Step 1:
Step 2:
Step 3:
