These are the old neopets sidebars. They are from a time when neopets had a good layout.
Altador Cup Sidebar
Just participate in the Altador Cup.
Altador Plot Sidebar
Unknown, but you probably need to complete at least Day One of the Altador Plot. Thanks to Neodigit7 on the Neoboards. :).
You can only get this sidebar on Neopets's birthday and on the birthday you set for your Neopets account. This sidebar removes the ads and gives you more random events. Sadly, you can't unlock it to use all the time.
Curse of Maraqua Sidebar
You must have participated in the Curse of Maraqua war and used 1 war point to buy this sidebar to use it.
Cyodrake's Gaze Sidebar
You must have guessed at least 2 or more right answers in the Guess Who Pushed Hoban page.
You have to win the Pumpkin Carving Random Contest or refresh Neopets at 11:59 AM on Halloween to unlock this sidebar. It was available to the general public for Halloween in 2006.
You must have had to complete at least 1 step in the Lost Desert Plot to get this sidebar.
Space Faerie Premium Sidebar
You have to win be a Premium member and refer 5 Premium members to get this sidebar.
Valentine's Day Sidebar
Send a "Mysterious Valentines Card" to another person on Valentine's Day to get this sidebar.
Claim the Advent Calendar prize (watch the animation) on December 31 2006.