How soon after takeoff can you recline your airplane seat?

A senior cabin crewmember here...

The "critical" times for flights is 3 minutes after take-off and 8 minutes before landing. This is the time in which the chance of having an emergency is relatively high, this includes some dangerous maneuvers as a result of rejected take-offs, wind shears, bird strikes, etc.

So, technically speaking if you count 3 minutes after the take-off roll then you are most likely safe enough to recline your seat. However, this is technically speaking and it's not what you should follow.

Legally/policy speaking, you can recline your seat whenever the seat-belt sign is turned off after take off, and placed back upright when the seatbelt sign is turned on for landing, or whenever instructed by the crew. Unlike what others have said, this is the correct indication to follow.

Some airlines allow their cabin crew to move around once the landing-gears are retracted, although moving around the cabin is a bit hard due to the angle of attack, but usually this means the airplane is in a somehow safe situation due to being away from the ground (at least 1,000 feet) and gained some air-speed. Again, this is not for the passengers.

Finally, the pilots have an access to a weather radar and sometimes they see a bad weather ahead so they delay the seatbelt sign because it would make no sense to turn it off for a couple of minutes before turning it again. So none of the "technical guidelines" would do you good, the only thing that will indicate that it is really safe is the seatbelt sign.

In Economy, I have always interpreted the "fasten seat belt" sign switch-off as the time it is safe to recline the seat. Sometimes, due to turbulence or other reasons, the sign stays on for long after take-off. In that case I tend to wait for the plane to finish its climb and stabilise before I recline the seat.

In Business with seats that turn into beds (such as those on international flights), I also wait for the "fasten seat belt" sign switch-off to move the seat to make myself more comfortable. I do not fully lie down until the plane is done climbing.

Interestingly, the FAA regulations actually mandate that the pilot must not takeoff until all seats are upright, while the passengers are only commanded to obey flight attendant instructions in the matter.FAR 121.311

no certificate holder may take off or land an airplane unless each passenger seat back is in the upright position. Each passenger shall comply with instructions given by a crewmember in compliance with this paragraph.

Takeoff is defined in 25.111 as

The takeoff path extends from a standing start to a point in the takeoff at which the airplane is 1,500 feet above the takeoff surface, or at which the transition from the takeoff to the en route configuration is completed and VFTO is reached, whichever point is higher.

So technically, after climbing 1500 feet (in most cases) you are out of "takeoff" and should be able to recline your seat. But guessing your distance climbed is difficult, so the chimes at 10,000 are probably your best guide, as mentioned by @Johns-305. Frequently these days I have also heard an announcement that larger electronics such as laptops can now be used, as those are restricted below 10,000 feet

In addition to existing answers, a couple of times I flew Upper Class on Virgin Atlantic, the pre-flight announcement stated that their Upper Class seats (which do convert into full flat bed) are certified for take-off and landing at any recline position and therefore there is no need to bring them to the upright position for take off and landing.

So, in this case, you can recline even before the flight starts.

The indication I've always used is the announcement that passengers may feel free to move around the cabin and/or the crew begin to move around the cabin. I've seen the seat belt sign illuminated for the entire duration of some flights, so it's not a useful indicator. Just because the air is rough it doesn't mean you can't/shouldn't recline your seat (unless the flight crew issues a specific instruction), but it's a wise precaution to keep your seat belt on whenever you are seated, hence the always-illuminated seat belt sign.

adding to more interesting answer , in india you you can recline anytime you want , it was yesterday when I travelled to spicejet flight and announcement was going on but i already had the seat recline and only heard the end part and flight was 4-5 sec from take off and even the crew saw me lying like that and she said nothing. guess its india maybe :P