In recent conflict of Russia and Ukraine some of G8 countries as sanction of Russian military actions in Ukraine declared they will stop preparation for G8 event in Sochi. But why would Russia be concerned about such statements? Is the G8 membership important? Do they even care about that?
There have been a press conference about conflict with the president of Russia and there was a similar question what he thinks about western countries reaction and possibility of withdrawing from G8 and here's his answer:
As for the G8, I do not know. We will be ready to host the summit with our colleagues. If they do not want to come – so be it.
Full press conference http://eng.news.kremlin.ru/news/6763#sel=43:21,43:32;46:1,46:29
Let's start from the very beginning. What's the history G7?
It was created in 1970's, with first 7 countries meeting in 1976. That was a meeting of the leading countries of the western world (or "free world", if you wish).
In 1997, when Soviet Union already falled, and Russia didn't have independent foreign politics, it was included in that club. But later, along with Russian reviving from the nightmare of 1990's, old standoff and contradictions come out again. That finally resulted in western countries decision to held 40th G8 summit in 2014 without Russia, transforming G8 back to G7.
For now, G7 finally become a western "gentleman's club" and nothing more. G7 even cannot form joint statement. Nowadays, it is a fragment of unipolar world, from the middle 90th - when nearly all questions in the world can be agreed and resolved in G7 terms - club of the winners of cold war. For now, it is just sort of an appendix.
Recently, Russia denied its involvement in G7+ summit project (which planned to include India, South Korea and Russia) - just because it is pointless to make a summit without China.
In fact, recently Russia offered a new format - of "G5" - meeting of a Securty Council members - which may be actual in the modern world
The G8 is made up the richest 8 nations in the world, representing about half the world's wealth in both GDP and PPP. The Group of Five-the five largest developing nations-are also often invited to meetings. More inclusive meetings include the G20. The leaders of the G8 meetings discuss global investments and loans worth billions of dollars that effect nearly every nation and person on earth.
They decide international global economic policy. For instance, since 2009, the group decided to privatize more of the world's global food investment. Around that time the world was struggling to meet increasing food demands. They agreed to the “G8 Action Plan for Climate Change to Enhance the Engagement of Private and Public Financial Institutions.”
The group may share data that can ensure the safety of one another citizens. They keep a list of pedophiles and international terrorists.
Other policy topics include: health, law enforcement, labor, social development, energy, justice and interior, and trade.
Russia would lose significant influence by being excluded from these meetings. Putin should care..a lot...no matter what he says in public. He might be able to meet separately with some of the nations, such as Brazil and China, but I think these nations would want to still be part of the G8+5, as well.
Source: Wikipedia "G8"