Linear campaigns try to follow a specific story or arc, and often seem like a movie where the GM acts as director. This can be a lot of fun, especially for one-off games, or games where everyone has the same idea when it comes to the direction of the campaign. Linear GMing can really shine in games that don't rest on world exploration, such as episodic games like Spirit of the Century (), or even while running a module in another game, be it D&D or Savage Worlds. Any campaign where there's a mutual acknowledgement of an underlying narrative.
Check the Label
That acknowledgement does need to be there, though. Linear GMing means that player choices will be curtailed. Exploring the Temple of Elemental Evil means not leaving and going hunting for the Tomb of Horrors. Going along with the scope of the adventure is part of the buy-in for players, but it's best made explicit, much like setting choices. This can help people understand the kinds of things they should expect from the game, and the kinds of expectations you may have of them. Mislabeling a campaign can cause tension. If players want to explore a sandbox world, and find themselves stuck to a specific arc, there's been a miscommunication.
Linear GMing vs. Railroading
Railroading is a four letter word when it comes to rpgs, but I think of it as linear GMing which isn't done as well as it could be. They're not necessarily equivalent, but they can be close. I think it begins to drift into railroading when the GM begins curtailing the players' ideas for solutions ("The door is bombproof. And antimagic), or forcibly directing them ("The cheese factory is closed, and no you can't break in"). Most rulesets don't necessarily allow for this kind of things, which makes some rulebending or breaking necessary to enforce the linearity of a campaign, and honestly, when the idea of enforcing linearity comes into it, it's probably railroading, and it might be best to talk with players about the kind of game they're interested in playing.
Linear GMing provides a clear direction for a campaign, which can help people focus on the action and on overcoming challenges in inventive ways. The constant presence of the narrative can easily provide interesting plot twists, which is something that can take a great deal more work with a sandbox or semi-linear style. Modules or pulp-style adventures fit into it really well, where the focus is on the action and not as much on the setting.
I don't think that linear games are sustainable. Sooner or later, people want to do their own thing, and a linear GMing style inevitably involves treating the players as an audience rather than as participants. They get to participate in the minutiae of the campaign, but they're not directing the story or altering the setting in meaningful ways without the GM letting them. It also means that there's an idea of how things should go, and with that a tendency to be frustrated when they don't go that way.
To sum up, I'm not a big fan of a linear style, but that's mostly because my preferences run toward long, exploratory campaigns. For shorter adventures, or as parts of a larger campaign, linear GMing has its uses.