Is there a maximum distance, duration or hours the driver will bring you? (I need to be somewhe ...

Uber, not on distance. Lyft, yes. Consideration for drivers.

(Updated: Uber has lifted this 4-hour limit.  This has been confirmed in multiple markets.)

Uber:

Uber does not enforce any limits to the distance of the proposed trip.  In fact, many drivers brag and compete on the crown for the longest trip made!

With that said, there is actually a duration limit of four hours (4 hours) that is enforced by the Uber app.  When the trip reaches 4 hours, the apps will notify the driver and rider, and the trip automatically comes to an end.  At that point, however, you are welcome to request another ride.  (Potentially your same driver can accept your request!)

Lyft:

Lyft has a similar rule in consideration for the driver.  Their limits are set by distance and price, and they are set differently for each city.  In general, they limit their trips to 100 miles and $200, at which point, the trip is interrupted and you would need to request another ride.  (The price limit is $500 for New York City and New Jersey, and $240 for Los Angeles - as of 02/2017).

Courtesy to the Driver

When requesting a ride for a long distance, you may want to notify and warn the driver of such intended trip.  This is for courtesy to the driver who prefer to not take such long trips for various reasons.  He or she may be at the end of a shift, may not want to incur the long drive back, etc.  Therefore, it is considered a courtesy to give the driver a chance to cancel the request.  

Source: https://help.uber.com/h/f7d602d3-f2c5-4d63-8395-83a8ea4c34d7

From Uber: "While Uber doesn't limit the distance you can travel on a trip, trips may automatically end after 4 hours. When this is about to happen, the driver is notified by the partner app."

ippei 1202

Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC