The growing importance of global governance institutions such as the UN suggests that nation states are not as significant as they once were. The UN has 193 member states and is able to deploy peacekeepers to state territory after a conflict, in an attempt to maintain newly established peace. It's members (general assembly) and more significantly its security council and the P5 can approve or condemn invasions and wars - a recent example saw P5 members deciding to work together to defeat ISIS (another non state actor) which has ultimately led to airstrikes in Syria. The UN security council is also able to impose sanctions and embargoes on nation states if it feels they have acted 'illegally', as with Russia's annexing of the Ukraine.
However, the UN as well as other significant global governance institutions (the three sisters), are made up of nation states and so cannot exist without the pre established member states. If significant nations states withdrew their UN membership, the UN's legitimacy and authority as a global governance institution would be severely diminished. Additionally the UN has no real sovereignty or law making power (it cannot make laws that apply to all nation states, but it can pass resolutions which have power over member states only), whereas nation states have governments with full law making power and the authority to impose these laws. The UN had no say over the US' 2003 invasion of Iraq which it saw as an illegal war, implying the US as a nation state is more powerful than the UN.
Regional institutions like the EU and NAFTA are arguably more significant than nation state actors. While the EU is made up of nation states, its members pool their state sovereignty. This effectively results in the EU having more sovereignty than its combined members and being able to assert its opinions as an influential global actor. It is able to influence trade and even fishing regulations and so has influence over the economies of nation states. The EU could be seen as an erosion of state sovereignty but its members are able to opt out and so its power is limited.
The growth of TNCs (which have become supranational in some cases) has seen corporations having enormous wealth and as a result, power as actors on the world stage. Some companies have a GDP higher than that of a nation state - Wal-mart, for example, has a higher GDP than Austria and South Africa. Moreover, TNCs create jobs wherever they decide to open stores or offices, and so the governments of nation states are forced to give them tax breaks to prevent them moving to an area which will make them more profit. TTIP, a trade deal which is currently being negotiated, would allow companies to sue national governments for imposing laws which do not allow them to optimise their profits, and would be a huge blow to state sovereignty. Additionally corporations are able to lobby governments as they have enormous wealth which can be used to influence lawmaking.
Nation states, however, provide the conditions of social order and security which TNCs need to operate so can be seen as significant actors in this way.
The rise of terrorist organisations like ISIS and Boko Haram is another factor which suggest nation states are no longer the most significant actors in global politics. ISIS has control over vast territories in Iraq and Syria, controlling areas with 2.8 million and 8 million people, despite not being a nation state. It has gathered huge wealth and economic power as a result, with nation states such as Turkey buying its cheap oil and essentially funding the operation. The lack of success of nation states such as the US, Russia and now the UK in taking down ISIS is a testament to its power as a global actor and has worrying implications for the fate of the nation state in global politics.