She's never satisfied
Why do we scream at each other
This is what it sounds like
When Dieffs cry1
About every two or three months on Garden Web's houseplant forum, someone will show up sounding alarmed because their Dieffenbachia, Philodendron, Monstera, or some other plant, is dripping water from its leaves.
If you are that person, and you've been referred here in response to that very question, don't be alarmed. It's good that you're paying enough attention to your plants that you noticed. A lot of people wouldn't. And to get the scary part out of the way first: it's harmless.
The phenomenon has a name. It's called guttation. There's a very good explanation of the phenomenon at this page, which I couldn't improve on if I tried (and I did try), so if you want the grisly scientific details in layman-readable form, that's the best account I managed to find.
Not all plants are capable of guttation; I think I've only seen it personally in the Monstera, Dieffenbachia, Ficus, and Philodendron genera, though I hear that Marantas do it too, as well as Alocasia spp. and several (many? most? all?) grasses. Monstera and Dieffenbachia are the most likely and consistent guttators, in my experience.
With Ficus in particular, the water exuded by the plant often has other substances (sugars, minerals, proteins, whatever) dissolved in it, which will build up over time to leave a small lump of white material on the underside of the leaf, or sometimes at regularly spaced intervals around the outermost edge of the leaves. On very large, old Ficus benjamina in particular, these deposits can get big enough that you might think they're a batch of mealybugs (I've been fooled more than once): the difference is more obvious with a magnifying glass, or you can get sophisticated and use the "squish test." If water comes out when you squish it, or if it kind of disintegrates, it's more likely to be a bug; if it's kind of waxy and solid all the way through, it's probably guttation. (Also mealybug fluff tends to be opaque, a shade or two whiter than white, and distributed kind of randomly around the plant, where guttation buildup is more translucent, very very light gray, and always on the same spot on several different leaves. It's subtle, but once you've seen both, it's pretty easy to tell them apart.) On Ficus benjamina, guttation buildup is always at the spot right where the petiole ends and the leaf begins:
Well, that's not the best picture, but it's a young leaf, so there isn't a lot of buildup to be seen. You get the idea. I couldn't convince any of my plants to guttate on demand, but it just looks like a water droplet on a leaf: there's not high dramatic potential anyway. I haven't had the weird waxy buildup thing happen with any plants besides Ficus benjamina.
The best way to induce guttation is to water a plant heavily, at night, when it's humid. I don't actually recommend this for houseplants: generally speaking, watering late is a good way to get a plant to rot, though some plants cope better than others. If you have a plant that is consistently guttating every time you water, this might signify that you're overwatering, but the cause-and-effect relationship isn't solid enough to worry about. If you are overwatering, there will almost always be some other, less ambiguous, signal that you're doing something wrong.
So guttation doesn't mean anything bad in and of itself. Your plant's just trying to freak you out.
1(from Prince's little-known first draft of "When Doves Cry." He changed it later when representatives from his record company said not enough people would know what Dieffenbachias were. It's a pity: if he'd left it alone he might have had a big hit.)