From an artistic point of view, 3D has a lot of potential that, unfortunately, hasn't been fully exploited yet. Most 3D films at the moment seem to be either gimmicky, with things flying at your face to provoke a reaction, or big budget blockbusters that just want to capitalise on the box office boost that the more expensive cinema tickets bring. Things flying at your face can work well artistically, especially in genre films like horrors that are meant to give you sudden shocks and make you flinch, but the real artistic merit in 3D is in watching it stretch away ahead of you. It should be like looking through a window.
Part of the reason, I think, for this problem is that there hasn't been what I like to call a 'not in Kansas' moment for 3D. Many other significant advances in cinematic technology have had a film that introduces the new medium in a smart way that really highlights the potential for what it can do. For example, the first film to fully use sound was the 1927 film The Jazz Singer. A few other films had managed to play sound effects and musical performances, but the Jazz Singer was the first to use synchronised dialogue. The film starts out with just the sound effects and songs being heard, and the dialogue shown with place cards as it always had. Then half way through the film, Al Johnson finishes a song, puts up his hand, and says 'Wait a minute, wait a minute - you ain't heard nothin' yet.'
The other big example is the introduction of colour in The Wizard of Oz. Again, the film starts off in black and white (or slightly sepia, if you want to be picky), which is what the audience were used to at the time. It would have felt familiar and not particularly exciting. The idea of colour is introduced thematically first in the song 'Somewhere over the Rainbow'. Dorothy sings about escaping her drab life to an unknown place that exists over the rainbow - somewhere separated from the real world by a barrier of pure colour. Then the tornado hits and carries her over the rainbow to Oz, and she opens her front door to a world of glorious technicolour. The audience is led through the portal into the cartoonishly bright primary hues of Munchkin Land, where every colour is richly accentuated to make the transition as overwhelming and magical as possible.
3D hasn't really had a moment like this. It started out as a gimmick, being showcased for its own sake rather than as a device to assist in the plot or art of the films it was used in. The best attempt I have seen was Coraline, which has some similarities to the Wizard of Oz - both are about a young girl who is not satisfied with the mundanity of her own life and escapes into another world that mirrors reality but ultimately has a more sinister edge. Coraline finds the other world by opening a small door in her house and crawling through a long tunnel. The filmmakers chose to make the 3D effects 4x deeper in the other world than the real world, and the tunnel is used to show that transition, so when Coraline first opens the door, we see the tunnel literally stretching away into the distance. The effect is deliberately unsettling and makes us as an audience instantly understand that the space we are moving into is not part of our world. Just like colour in Wizard of Oz, the 3D helps distinguish one space from another and helps us understand in a subtle way which world we are in at any one time. This becomes useful later on in the film - initially, Coraline is able to return to the real world by falling asleep in the other world, but when things start to go bad she tries to escape this way and it doesn't work. The audience can tell something is wrong when she wakes up because of the depth of the 3D, despite the fact that her bedrooms in the two worlds are relatively similar. The Wizard of Oz is actually undergoing a 3D re-release at the moment, and if they didn't use this technique in the conversion then they're definitely missing a trick.
Unfortunately, despite critical acclaim and reasonable box office success, Coraline did not have the impact that it needed to have in order for the effect of its Oz moment to resonate in the film world. Other films have gone a lot further to show that 3D can improve a movie on an artistic level, most notably Avatar, Life of Pi and Gravity. All three have been quite rightly recognised as technical and visual masterpieces, with the latter two cleaning up quite nicely at the Oscars. Gravity was particularly impressive, using 3D to show both the vastness of space, with the curvature of the Earth stretching away into the distance in the background, and the threat of the shrapnel that flies at lightning speed past your eyes. It has also been used to great effect in animation, with films like Up, How To Train Your Dragon and the Lego Movie, which can be created in 3D from the start without the need for expensive specialised cameras.
I think part of the problem with 3D, which wasn't such an issue with more fundamental artistic tools like colour and sound, is that it is less obvious how to work it into the language of film. People are still finding ways to make use of it, but to do so they need to be experimental and try things out to see if they get the desired response from an audience. However, at the moment 3D is only really being used in big budget blockbusters and animated family films, which studios rely on for the majority of their profits. They won't want a director to experiment on something that they are putting hundreds of millions of dollars into in case it doesn't work and that money is thrown down the drain.
In order to get experimental with 3D then, it needs to be used in the lower budget films. This doesn't happen at the moment as the technology is so expensive - again, studios won't want to spend loads of money on a 3D camera for a film that they don't expect many people to see. Fortunately as the technology is developed, the more basic 3D cameras will become cheaper and more accessible to smaller studios, so we should start to see more interesting use of the medium. If an idea is tried and it works, it can then be picked up by the bigger films and will end up written into the artistic language of cinema.
The developing technology will also help overcome the more fundamental problems audiences have with 3D films at the moment. The biggest one is the higher price, which is predominantly down to the cost of the screens and projectors required to screen 3D in cinemas. As such screens and projectors become more commonplace, the need for the higher ticket price should diminish, which should at least stabilise the price and may even cause it to go down a bit, even if 2D always remains cheaper. People also don't like the glasses, which are necessarily dark and so diminish the colour spectrum available, as well as being awkward if you already wear glasses. The technology already exists to show 3D without the need for glasses - for example in the Nintendo 3DS - so the next logical step is for this to be expanded and utilised in cinemas. Some people find themselves getting headaches from 3D, but this can be reduced by the higher frame rate that was explored in the first Hobbit film, and again may be helped if the glasses become obsolete.
Another argument that I have heard against 3D is that the focus of the lens is often honed in on the one thing the filmmakers want you to look at, with the background being too fuzzy to make anything else out. This prevents people from admiring the work that goes into the set design and so on. For example in the image below from Clash of the Titans, Ralph Fiennes' Hades is in good focus but the decoration of the room he's in is clearly intricate but hard to make out in any detail.
So in short, 3D has a huge amount of potential, but in order to reach it the technology required to create and screen it needs to be better, cheaper and more accessible. The only way that will happen is if people are working on developing that technology, which will only happen if they get paid to do so, which will only happen for as long as the studios that pay them continue to believe that it is a worthy investment. That in turn relies on audiences paying to see 3D films. The more people dismiss it as a gimmick and not worth the extra money, the more it will be used as a gimmick to create films that aren't worth the extra money. So don't give up on it just yet!