When people talk about monopoly, means that some brand of some sort of stuff dominates the market.

But is there a percentage of market-share that define monopoly?

Can we say that DS has the monopoly of handheld market and Wii will have the monopoly when it reaches the 50.1% market-share?

No, in fact monopoly = one company on one market.

Monopolies exist when there is no competition and one company rules the market. Even in the portable market, there is plenty of competition. Monopoly would be at least 90% market share or more.

@wiistation360: no, that would be an oligopoly

So why people used to say that sony monopolized the last few gens with Ps1 and PS2?

Sony basically had one for two gens. It wasn't a total monopoly but it damn near killed Nintendo off

I would argue it's not related to a particular percentage, but to what it means you can do.

MS has just under 90% market share in the OS market, and yet I wouldn't consider it a monopoly due to a lack of two main things
The ability to drive their competitors out of business if they wished (and believe me, they are trying their hardest to stop people turning to Linux or Mac)
Creative control over the direction and pace of advancement of their industry

DEFINITION: (economics)
A market in which there are many buyers but only one seller; "a monopoly on silver"; "when you have a monopoly you can ask any price ...

Isn't it a board game where you have to buy properties. And end up getting frustrated and end up throwing houses and hotels at opposition players.

A monopoly is one company exclusively providing goods for one market. In the real world, this is accompanied by domination of the market. In a monopoly, the company with the monopoly will control the market so as to prevent other companies from entering it.

People often use the term monopoly in hyperboles:

Sony had a monopoly for two generations => Sony practically had a monopoly... OR it was like Sony had a monopoly...

When the DS reached 50.1% market share, it took a majority market share. It seems to me as though you may be confusing majority and monopoly.

The current handheld market is a duopoly, if anything. If Nintendo were abusing their market share to best Sony, you could also say that they were monopolising the handheld market, i.e. turning it into a monopoly. If Sony closed shop, and Nintendo continued anti-competitive practises to prevent others entering the market, that would be a monopoly.

Nearly all home consoles and handhelds have been sold in oligopolies.