Just like human generations, new gaming generations can begin while another is still going on. Generations don't end until all consoles released in that generation stops production. It's foolish to think otherwise.

6th gen started with the Dreamcast, 7th gen started with the 360, 8th gen started with the WiiU the first console released is the start of "next gen".

If we go by when they stop being manfactured does that not still mean we are stuck in the 6th generation as the Nintendo DSI is still in production (I think)?

Personally, I would say the cutoff is when the next gen hardware is released which began with the Wii U (arguably with 3DS and Vita as well if we count handhelds). We can argue about the power of the Wii U, but that doesn't matter unless we are using some sort of graphical power standard to say which generation is which now.

The wikipedia article seems to believe in the "stopped manufacturing" standard as it states that the 6th generation ended in 2013 (when PS2 was discontinued). Of course,  this does not count handhelds.

Handhelds and consoles are treated as separate industries within the overall gaming industry, so the 6th generation of handhelds is still going on while the 6th generation of consoles ended when the PS2 was discontinued. Also, we're not necessarily stuck in the 6th handheld generation, more so that it's still going while the 7th has started.

If we want a definition that prevents overlap, I think a good (albeit slightly ambiguous) definition would be: When the next generation starts selling better than the current generation. It's a definition that puts the focus right where it belongs. That said, this definition has its problems.

When at least 2 of the 3 consoles are no longer manufactured and most games don't come for any last gen system, so for example with the 6th gen that ended in 2009/ 10 when PS2 got hardly any new games. But currently we are in between the 7th and 8th generations

Well, I'm glad you know what consoles were the first of each gen. However, the question asks when does the generation end

@Max

Does it matter? Is it because when it ends your system "wins".

Generations overlap, so I say a generation is defined by three periods:

1. The early period when not all major competitors are out
2. The main period when all major competitors are supporting their systems
3. The late period when a new generation is out

In this system, the production of a piece of hardware defines when a gen starts and ends. Therefore, I believe that a generation only ends when production of relevant hardware ends. This means the PlayStation 2 generation only ended recently, but what're gonna do?

I say it depends on whether you want the ps3 to potentially win this gen or get last.