What would happen if America withdrew troops globally?

As for what would happen.

In the pacific, two possibilities. Pacific nations such as Singapore, Australia, the Philippines, Japan, South Korea, New Zealand, and others form their own defensive coalition to check Chinese influence in the region. The US loses influence in the region, but China gains little and the independent coalition deals with both powers. If the coalition fails, or is never formed, it's very likely that Chinese hegemony prevails in the Pacific. The smaller nations, many of which already have China as their main trade partner, would also be beholden to China for security. This gives China very powerful influence over the pacific nations, and makes the US the outsider. Pacific trade and politics will be on China's terms.

In the Middle East. Saudi Arabia is already preparing for this contingency. Maybe not to much change there except less favorable oil prices. They will however continue their political and ideological war with Iran. Without US support on SA's side, Iran and likely ally Russia make significant against Saudi Arabia and their regional allies. Continued strife in the region may even erupt into a formal war between nations. In any case, Turkey, Iran, Syria, and possibly Iraq will all move further toward Russia.

In Europe. Western Europe is able to check Russia to some extent, but eastern European nations are on shaky ground. Several of them likely reenter the Russian sphere. The Baltic states may try to align with a Scandinavian pact, but the entire region will find itself in limbo, torn between wealth of Western Europe, and the force of Russian arms.

What does this all mean for the US?

We lose influence around the world. Security treaties, economic bargains, and political leverage all become more difficult for the US. Ever notice how almost every major US military endeavor since WW2 has included Australians? Won't happen anymore if they're busy with their own security, or under the Chinese political sphere. US economic investments abroad become riskier in regions where the US doesn't wield as much influence. Investment in US interests also becomes less attractive for foreign investors, for a similar reason. The US is less capable of advancing it's interests in the global market. Nations don't cooperate with one another out of charity or civility. They do it to advance shared interests. If the US withdrawals from the world (not just militarily, but economically as well), then other nations will have fewer shared interests, and less motivation to cooperate.