option 1) install a drain tile system to the back of your lot, into a 'dry well' filled with gravel. You may either use that corrugated black pipe or conventional pvc (more durable IMO), then either let the water fiter through gravel area to the pipe or install a collector grate

option 2) similar to above but use a pop up emitter run either the back of the lot or near the curb

option 3) would be run the line to the curb and core a hole in the curb so it dumps in the gutter of the street.

here are some links with pics and tips:
http://www.askthebuilder.com/407_Dry_Out_Soggy_Ground.shtml
http://www.askthebuilder.com/B175_Soil_Drainage_Solution_French_Drain_Systems.shtml

Thank you, jason. I think I have a new way to approach the city on this. I dug out our topographical survey and the one we were given when the house next door was proposed. Their survey doesn't show the "hole" at all. Ours, dated 1995, shows a roughly 20 X 60 depression. I'm hoping we won't have to remedy the problem, yet it will have to be fixed somehow.

The depression is at 79.69. The surrounding land is 80.50 on both their side and ours. The edge of the creek is 71.00.

What a plumber proposed was to run a pipe (150 feet) along our west lot line to the back lot line (south). It would have holes at the far end and a gravel bed underneath. Water would then have to make its way to the creek (east). Alternately he would run a diagonal line across the back yard (250 feet) to the creek. Both of these require a backhoe to trench. (I'm picturing a big mess AND a big bill.)

If the city will permit it, we could go 100 feet north to the road and hook into the city's storm sewer, which empties into the creek. This might be done without trenching. (There is no curb on our countrified street.) This would have to run on a bit of a diagonal to miss our 100-year old elm.

I'll try to make an appointment with the city tomorrow. I just don't see that this should be our problem. Either the neighbor's surveyor did a bad job, or the city missed this, but WE didn't cause this. Our mature ash tree is surely dead from standing in this water and our wood fence posts will rot.

you could hand dig it and have a few friends help, even rent a ditch witch for a day.

If the dip is entirely on your land it might be cheaper to fill it.

As for the tree being dead its iffy, but depending on where you are at it may be best get rid of it anyway.

Also just curious why no one ever bothered to correct the grade.

If the backhoe operator is careful the mess will be minimal.

Jason, you are so nice to come up with good ideas.

I don't think we could fill it in without causing our basement to flood. There's the new house West of us, then the hole, then our house, then the creek. If we fill it in, wouldn't the water seek the nearest lowest place? (Our basement.)

I was so amazed today. After calling a waiting for a month someone from the city showed up today to actually SEE the problem. One man's idea was to create a swale north of the hole, toward the street. I guess that would spread the water out and it could evaporate or sink in faster.

The city keeps saying this and that and how the neighbor's house was built to code, etc. However, da facts am the facts: we have a stagnant pond where there was none before. I said that I'm not interested in fixing blame, just getting this pool of water moved. They promise to get back to me THIS WEEK.

Nobody bothered to correct it because it was no problem until this year, post-new-house-next-door.

I would be inclined to say that if your foundation drainage is in good shape it should handle the water and if the basement was sealed properly it should not leak. BUT sight unseen please don't quote me.
Often basement sealing, drainage and gradation issues are not given proper attention by contractors.

This is a former marshy area that was drained, probably 90 years ago. The "creek" I referred to was just a tiny tributary that was dredged back then.

Our house is built on the foundation of a 1950's ranch. There are some signs of leaks that were repaired -- on the west and SE basement walls.

The SE corner of our acre lot is in flood plain and stays wet into late May/early June. There is a development south of us that is about 15 years old. It has several conservancy areas that have drains that empty into the creek -- fortunately downstream of our property. EVERY house in the city has a sump pump.

There is a swath of odd soil that runs from west of our house, all the way to Lake Michigan (a mile). Our GC ran into it when building the foundation for the screened porch on the SE side of our house. Our neighbors' GC also ran into it. This is the strangest soil I ever saw. It's looks "greasy". We have odd water bugs that come up the basement drains and head for the light of a window well.

(Just wanted to give you the picture of our water issues!)
Maybe I'm being prepared for a life in Holland?