Today I find my lenovo laptop power adapter's output negative terminal is not grounded (the input ground terminal is not connected with output negative terminal, measured with DMM). But another old one is just opposite, the output grounded. Why? There is any standard for power adapter? If the laptop is not grounded, is it safe?
My experience is that the power supplies for the older laptops in which the backlight was CCFL were usually grounded on the DC side as well. I suspect it was because of the high-voltage inverter needed for the CCFL (approx. 600V DC output), but I'm not entirely certain that was the determining factor. There's a concrete example of an older HP I have that does have minus grounded; details on that in this superuser post.
The newer laptops with LED backlight tend not to have the minus pin grounded. There can be static buildup and leakage currents on the non-grounded laptops [the latter particularly on metal cases] which can be irritating to some people. See this discussion on MacBook and this video of an actual measurement; he only measured AC voltage from case to ground as 78V AC with no grounding, which is probably enough to feel a slight tingle on a leakage current. A better test would have been to measure the leakage current as well... but I guess you need to try harder finding EE pros among Mac fans.
If the laptop is not grounded, is it safe?
Some laptop adapters don't have an earth pin and therefore they can never have a grounded output. It's not a problem providing that the insulation and clearance/creepage distances inside the adapter are adequate.
If a laptop uses a grounded adapter and the adapter is unplugged from the laptop then, the laptop isn't grounded - it's clearly safe in this scenario and, just as safe as when plugged into a properly designed and manufactured adapter that doesn't need an earth pin in the AC plug.
The first thing to understand here is that the AC ground coming from the wall, does not serve the same purpose as the DC ground going to the laptop.
They both typically sit at 0V and are often physically connected, but they serve different purposes. The DC ground is used to complete the circuit so power can flow, the AC ground is used for saftey, the power flows between live and natural and, under most circumstances, won't touch ground at all.
The AC ground is used when there is a fault. For example, say the live wire came loose and touched the casing of a metal microwave. If anyone touched the microwave, the AC power would flow through them and most likely kill them. To prevent this the casing is connected to the ground wire, so as soon as the live wire touches the casing, a massive current flows through the ground, which blows the fuse / trips the breaker, isolating the device.
This ground connection is not necessarily needed if the device is suitably insulated. Phone chargers often don't have a ground pin (or for me in the UK, they have a plastic one) because if a wire did come loose, there is very minimal chance of shock as the whole device is insulated.
In your example of the laptop charger, the AC side of the charger often has a ground pin. I'm not sure if this is required or if some manufacturers are just being extra careful. However the DC side of the charger does not require one, as it is insulated very well from the AC connection, if the live wire came loose inside the charger, there is no way it could make your whole laptop live, so there is no need to ground your laptop.
Some times the manufacturers simply ground the whole ground plane within the charger, which the negative terminal of the charger is connected too. This is why sometimes you see a connection, and sometimes you don't, it's not needed at all, it just happens sometimes due to every 0V being connected together.