Most campaigns are OK
This is not such a problem from the campaign point of view. Most campaigns could be played with more characters without much problems (apart from, maybe, the level of the combat encounters). We are also used to stories with big groups (think of the Fellowship of the Ring or the Heroes of the Lance).
However, this is a problems from the human point of view, or the Dungeon Master vs players point of view if you will. Most other answers have given hints about what to do as a DM, not about what campaign fits a big group. This makes sense, because a big group is a problem for the DM, not for the campaign.
I am going to suggest another way of dealing with big groups based on my experience.
Two Dungeon Masters
The tradition of RPGs assumes that there is only one director, but this is not written in stone. I have played with two Dungeon Masters in the past with good results. I have co-directed groups between 5 and 12 players.
The benefits of playing with two Dungeon Masters are many, including:
- Faster combat. One of the worst things of a DnD combat with 10 players is that it takes forever from one action to the next. Two DMs cut the time in half and make combat much more fluid.
- Split the party? Why not? One of the RPG mantras of all time is "don't split the party", even if it makes sense from the story point of view. This is because it is a nightmare to take care of two different groups if you are only one person: one of the two groups is waiting and bored. With two DMs this is not a problem at all.
- Better NPC interaction. With two DMs, you can have both a narrator and an NPCs talking at the same time, or two NPCs talking at the same time. This makes a much more believable story.
- Efficient use of rulebooks. Ever found yourself on a discussion about the rules? There is no good way of doing this: either you continue with the story a the expense of correctness, or you look up the rules at the expense of the story. This is not a problem if you have two DMs: one continues the story while the other checks the rulebook(s) at the same time.
- Additional effects. Taking care of the story, the maps, the music, and everything can be difficult if one person must take care of everything. With two people it is easy.
It takes a bit of adjusting to each other the first time you try it, but if you have a good personal relationship with the other DM (which I assume is always the case) you will quickly find a good balance.
Final word: adjust the level of combat encounters
In DnD, the challenge of the combat encounters is an important fun factor for most groups. DnD 3.* assumes that most parties have 4-5 members. If your group is twice as big, your should enhance your enemies accordingly so that they prove challenging enough.