Solution 1:

Updating the servers has to be done by the server owners manually. Until they do, your game will show the servers as outdated in your multiplayer menu. Note that Minecraft Realms are automatically updated by Mojang to the latest release. There is nothing you have to do to upgrade a realm.

Another thing to note is that unlike most modern games, you can always choose to play an older version of the game by choosing one in the profile editor of the Launcher.

To do so, open the Launcher and click on Edit Profile in the lower left corner. Under Version Selection there's a dropdown box labeled Use Version. Choose the version for your servers from that list and start the game to play with your friends.

You can also make a different profile for each version you play, for quick access.

Final word of warning: Be careful to not open worlds you played in 1.9 in 1.8, as it might break things.