I can't speak for everywhere, but most dumps in Canada eventually become parks or reclaimed land. Gases from rotting garbage is siphoned off and in many cases used to create electricity, to power the park ie washrooms, lighting and in some cases the park equipment such as lawn mowers, snow blowers.
Every landfill has a lifespan. This is based on the containment field, size and so on... Not sure what Fresh kills are...
Many cities are now creating less 'garbage' and are collecting compost-able materials, recyclable materials and so on. In my city, they have put some serious goals into place and within the next 10 years, 90% of garbage will not be put into landfills.
We are already recycling upwards of 50% of paper, metal, glass and plastics. Electronics are being collected separately and while it was once common place to send this material to Asia, this is now frowned upon, and I do believe illegal in many provinces and states. Compostable stuff is being made into compost and resold at plant stores as mulch and so on... and these markets will only continue to grow.