What is the opposite of a "crown" (in the topographical sense)?

You're talking about camber, which is the curved cross section of a road, and so i think the answer is reverse camber. It's called "reverse" because the standard camber is to have the road rising in the middle, as you say, so that rainwater runs to the sides.

There's a slideshow on this here. http://www.slideshare.net/kushalpatel91/road-geometrics

As well as the curved cross section of a straight road, when a road goes round a corner, it is often built so that the outside corner is higher than the inside, so that the cross section is a diagonal line. This helps the stabilty of cars taking the corner, especially at speed. Sometimes a corner (not by design - usually just in rough country roads for example) will have camber pointing the opposite way, and this is called "adverse camber". This will tend to dramatically decrease the stability of a car taking the corner at speed.

"Camber" is used in other contexts to talk about a curved cross-section, such as snowboards.

Around here that's commonly referred to as a swale. The dictionary definition implies that it is a low, marshy depression, but the farmers here don't read the dictionary and they apply it to any shallow valley which directs rainwater.

cupped

cupped (kʌpt) adj
hollowed like a cup; concave

cupped. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved April 7 2016 from http://www.thefreedictionary.com/cupped

The opposite of a crowned road surface is a "banked" road surface. This sense of the word "bank" is defined by oxforddictionaries.com as

[to] build (a road, railroad, or sports track) higher at the outer edge of a bend to facilitate fast cornering.

Since the questioner himself mentioned this term in a comment on another answer, though, it's possible that this term has been considered and rejected.

I don't normally reply to things like this, but given what someone who is still an engineering student brought to my attention and the fact that this thread is now a top google result to the question of what reverse crown is ... I feel the need to add my 2 cents.

Yes, it is commonly referred to as reverse-crown or reverse-crowned. Especially amongst architects and some contractors. Swale is another acceptable and common term. Reverse camber would technically be correct, but I have never heard that term used for pavement.

But DO BE CAREFUL. In engineering (where unfortunately there's a historical trend of using the same term for different applications like "runoff" and "runout"), reverse crown has another specific meaning in terms of pavement cross-slope.

Normal Crown is an easy concept. A crown. A peak. The roadway slopes to either side. When a roadway enters a curve there must be a transition to where at the "center" of the curve the cross-slope is equal on both sides of the centerline, giving one long continuous slope from edge of pavement to edge of pavement.

For example ... "Normal Crown" in most situations is where both sides of the road slope downward at 2%. Or ... Left = -2% and Right = -2%. The negative indicating a slope downwards from the crown/centerline. One possible scenario is that this roadway at some point could be at "full superelevation" at a cross-slope of 6% (just picking a number for an example).

The cross-slope transition for a right curve would follow: left cross-slope increases at a consistent rate until it is opposite the right cross-slope. That is: Left = +2% and Right = -2%. THIS IS WHAT IS KNOWN AS "REVERSE CROWN". Despite sounding a little counter-intuitive.

Then both sides change in cross-slope simultaneously until "full superelevation" is reached. So L=+3%, R=-3%; L=+4%, R=-4% and so on until the full design cross-slope is achieved.

I'm saying all that to say this ... If you tell someone that you want a roadway or parking lot "reverse crown" you better ensure you mean the same thing, because it may result in either a swale or having the entire pavement slope to one side.