The ADS-B signal depends on the transponder on board of the aircraft. Most new aircraft have an ADS-B capable transponder, and in most cases the ADS-B function will be active. This it not something that is decided on a flight by flight basis, it's basically off or on (you can't switch it from the flightdeck
AFAIK, unless you switch the transponder to off).
ADS-B is not necessary for international overseas flights, but it is mandated in Australia, above certain flightlevels over Hudson Bay in Canada, and in few other areas in the world.
The US rule is mandating ADS-B in 2020, Europe will most likely mandate ADS-B for new aircraft from 2015, combined with mandate to retrofit ADS-B from the end of 2017. However the rulemaking is not yet passed by the European Commision so these dates might change, although I think that's unlikely.
Assuming you have a SBS-1 station or something similar, note that not all aircraft that you see are sending the correct position. Some aircraft send their IRS position, which can be several kilometers off. This is indicated in the ADS-B position message by an integrity flag set to 0, but unfortunately the ADS-B stations that are commonly used for hobby purposes don't show this information.
Under the mandates (Australian, Canadian, European & US) the position source must be GPS (or a source with the equivalent or better accuracy & integrity, at the moment only GPS qualifies). In general an integrity number of 4 or 5 is needed for the ADS-B reports to qualify for ATC surveillance purposes.
Another thing is the ADS-B protocol version: Europe & the US will mandate version 2, while the aircraft that are equiped now use version 0 or 1.
Best,
ATCast