If you've got the proper sloping, clean and clear working gutters and downspouts, there's only a couple of other 'cheap options'.
Take a look at what happens to the water that comes out of the gutters/downspouts and the water that comes from your 'uphill neighbor'. If the answer to either or both is: It drains back towards the crawlspace, then you have your answer (so to speak.) THe water from the downspout needs to be 'take away'. Either build a dry wall or bury some perforated pipe to take it elsewhere (via a french drain.) THe same goes for the water coming from your neighbors. In short, the water is pooling in a 'low spot' most likely due to the ground around it being saturated. If it wasn't saturated, I'd bet it would just leach through as it does in a 'normal rain'.
For info on surface drainage in addition to a link on how to construct a french drain, see Landscape Drainage. My best to ya and hope this helps. (If you have more question, ask away.)