First of all, note that this is not a list of the top 7 expansions. This is a list of games that are good alone, but great with an expansion or expansions, and a list of games that might be ok by themselves but become better with expansions. Either way, the expansion(s) to a game make it better than it is by itself.
#7 Settlers of Catan
I enjoy basic Settlers. I enjoy Settlers with Seafarers and/or Cities and Knights more. The other expansions have their merits, but they're not as good in my own opinion. Basic Settlers is a fine game, but it needs a little extra something to make each resource feel important. Seafarers gives sheep an added importance while C&K changes up the game in many ways. These do add time, but I think that either is worth including to make the game better.
#6 Formula D
Expansions to Formula D are new tracks to race on, but the thrill of racing games is learning how to race on new tracks. If you race on the same layout every time, eventually you know exactly how to best get around, provided your dice cooperate. Being able to race on 8 different tracks gives me a lot options right now, though more tracks would be nice to have.
Specifically the Pied Piper expansion. The base game comes with 6 powers, but you use all 6 in every game. That leads to some strategies becoming dominant, and samey gameplay. Pied Piper adds 12 more powers, yet you still only play with 6. That really changes up the game and leads to a lot of variety between games.
Carcassonne has many expansions, very few of which are necessary, but several of which enhance the game in some way. Basic Carcassonne is a fine game, but it really needs the first expansion (Inns and Cathedrals) to make it a more strategic experience. This is a game where you can't play with everything every time you play it, the game would take too long. Adding in some expansions makes Carc a more enjoyable game, just don't go overboard.
On the Brink changed Pandemic in so many ways that one could argue that it is an essential expansion. OtB more than doubled the available roles that players can use to try to win the game. This alone would be an expansion worth owning, but when you add in several new ways to play the game, OtB greatly enhances Pandemic. I liked the basic game of Pandemic, but after 20 plays, I needed something more. OtB made it harder in ways and easier in others, which when combined made for a much more enjoyable gaming experience.
Though I own every expansion to Dominion, I won't argue that they are all necessary. However, adding in at least 1 expansion makes Dominion a better game. Each set has a general theme, so the cards in any set tend to combo well with each other. Once you start mixing things, the combos get more interesting, and setting up a deck becomes a bigger challenge. The nice thing is that the choices in any given game don't expand a lot, but the variety of games goes up exponentially. So for not a lot of extra difficulty, and a lot of added replay value, Dominion is the #2 game that gets better with expansions.
This game would be nothing without expansion ships and upgrades. They are what makes this game compelling and challenging. In ways this is cheating since it's a miniatures game. You have to have multiple units for it to be playable, but the game does have a core set that works on its own. There is fun in that single box with 2 Tie Fighters and 1 X-Wing, but adding in more ships truly makes the game special.
For links to many of these games and their expansions, click on the BoBG store link in the header.