Alright, here's one of my really old ones for your enjoyment. Herman Kahn and anthony J. Weiner's "The Year 2000: A Framework for Speculation on the Next Thirty-Three Years." is quite a goldmine for map ideas. The scenario I picked is one of his eroded democracy ideas where renewed communist expansion and de-legitimization of normal democratic processes create a crapsack world.
The divergence? Oswald's shot misses and Vice President Johnson is the man who dies. The changes begin to mount as Kennedy picks close personal friend and works out a relatively short-lived compromise peace in Vietnam. The peace lasts six months before northern troops are in Saigon and a massive revolt happens in 1967, after the third failure to pass a civil rights bill. Following the unrest, the "Kennedy doctrine" is formulated wherein America will focus on cleaning up it's own domestic affairs and dealing with the reds at home. Things go downhill from there with Europe choosin to disengage from the US. Besides Europe's beginning a new policy of detente, the communist powers quickly move to take advantage of America's move towards isolation and internal recriminations. During the period of 1967 to 1990, much of the third world fell to some form of communism, or if they were lucky ended up a neutral nation. Whether it's Castroism-Guevarism, Afro-Socialism, Maoism-Third Worldism(a modified form of Maoism formulated in the 1970s after a different leader wins the post-mao struggles) or orthodox communism, the international communist movement enjoys a renaissance. This renaissance is further aided by increasing cooperation among the parties in the formation of the "Joint Dictatorship of the Proletariat and Oppressed Nations", to act as a new comintern. This has impacts on Israel's wars, which led to the nation being a shrunken remnant of it's former self. India and the nations of Europe responded to these developments by forming a new group of their own of more democratic states. When America re-emerged from it's hermit kingdom foreign policy, it reentered a very different world.
The world's current events are defined by the non-communist powers slowly reconciling and coordinating their activities. The "Non-aligned movement", Japan, The United Arab Republic, The Islamic Republic of Iran and even the United States are cooperating to attempt a rollback of the communist gains. Interventions to expel the reds from part of Malaysia, half of Nigeria and Colombia have succeeded. Only massive nuclear saber-rattling has prevented further large-scale liberation attempts. Most experts agree that there is a real possibility of a large-scale war within the next five years between communists and capitalists.
Around the world, there are certain commonalities that evolved after the divergence. The first commonality is the prevelance of brutalist and other austere architectural styles. This is caused by a worse world economy combined with a much larger communist block. The old democratic principles of representatives voting on legislation have eroded, with large-scale protests setting public policy in many nations. This conributes to making democracies more unstable, and allowing domestic radicals of the left within the west to point to 'stable' and 'orderly' communist regimes as a good example. The relative lack of civil liberites worldwide is another example of responses to unrest; there are security cameras everywhere and many ostensibly 'democratic' nations have political police whose goal to make sure elections are 'fair'. Economic policies tend to favor statism, even in capitalist nations where the main difference is that the state aids large companies. This is a world of large state-run combines and megacorporations. The worse economic policies, combined with no boom in international trade have hurt economic development along with investments in technology. This means that technology on average is 5-10 years behind and anywhere from 3 to 4 times more expensive than it would be at the real world's equivilant technical level. Ideologies of national liberation have proven more important than in the real world with Hawai'i, Puerto Rico, Quebec, French Polynesia and Okinawa all being independent.
America, 47 years after the death of President Johnson is a very different place from 1963 America, or even the nation of the real world. America never opened immigration back up and is white, poorer and much more protestant. America is currently in a religious phase with fire-breathing evangelicals enjoying unquestioned majorities of public support. This shows in many of the social policies such as draconian anti-crime policies, a federal ban on abortion, enforcement of sodomy laws, mandatory school prayer, banning teaching evolution, etc. It's allies consist of right-wing dictatorships, Australia and an Israel that barely survived the war of 1973. Other notable American allies are Legitimist Spanish and Portuguese dictatorships that survive in their African colonies. Due to Johnson's death, the civil rights movement didn't have the stroke of good luck it enjoyed 1964-66. Sadly, this means that the question of whether blacks are people or not is still an open and bitterly divisive political question. Most presidents since 1960 have been Democrats with the only republican serving a term in 1985-1989. The Democrat party that emerged in the wake of the Kennedy and Smathers administrations was a quite conservative party that opted to purge it's left in a reversal of the post-1968 expulsion of the wallacites. The twin ineffective oppositions are the Republicans who act as a moderate quasi-libertarian party and a highly radical Progressive party born after Martin Luther King Jr.'s successful merger of the black liberation and peace movements.
Life in the communist countries follows the traditional pattern of red regimes. The one difference, is that with large resource rich areas newly acquired for the communist sphere, the standard of living is better and they are actually able to (sometimes) feed themselves. There has been limited economic reforms in the early 2000s, after the economic gains from adding large portions of asia, latin america and Africa to the sphere and favorable trade terms with "Non-aligned nations" began stalling out. The types of reforms that are allowed are anemic, weak and kept limited due to the party having more true believer than in the OTL 1980s soviet union. However, not all communist nations have joined the Joint Dictatorship of the Proletariat and Oppressed Nations; Yugoslavia struck out on it's own and North Korea decided that siding with India's proposed 'non aligned movement' was a better deal for the house of kim than being either a Soviet or Chinese vassal.
Europe is poorer, less militarized and more left-wing than in the real world. Communist, social democratic, labor and green parties tend to have strong roles in governing coalition with important effects such as foreign policy. The European Union is rather closer to federalism than in the real world because of there being fewer members to oppose it, combined with a smaller germany meaning more equal population numbers across the European union.
India and the rest of the non-aligned movement tends to be more lefty than in the real world. This ranges from left-leaning multiparty democracies like India or Quebec to open communist nations like North Korea or Yugoslavia that for whatever reason don't want to side with more 'orthodox' communist states. Alot of these nations tend to be "democracies" where one party consistently wins.