First the assassinations:
Michael Collins - Had he lived Irish history would have changed completely. de Valera wouldn't have dominated irish politics for 30 years, and there would have been no Fianna Fail dominance (and consequent arrogance and corruption) so a healthier irish democracy. Collins was a believer in free trade, and the need for ireland to industralise to become competitive, there would have been no 30s trade war, and the economic reforms proposed by Lemass and Whitaker would have happened a generation earlier. So rarely is there a case of one man's death having such an overwhelmingly negative effect on his country
Huey Long - A big AH favourite, had he lived i doubt he'd be able to ensure Roosevelt's defeat in 1936, but come 1940 or 1944 he would become a major player. Bare in mind he was 3 years younger than Dwight D. Eisenhower, he might not necessarily have become President in the 30s or 40s. Intriguing what his role might have been come the desegregation battles of the 50s though, would he have become a demogogue like Wallace or Thurmond, or sought to be a moderate on civil rights in order to remain palatable to the wider electorate?
Airey Neave - Escaped from Colditz and became a Tory MP, responsible for Thatcher's victory in the 75 tory leadership contest and shadow northern ireland secretary when he was blown up by the IRA. His tenure at northern ireland would have been interesting.
Other deaths:
Jose Sanjurjo - had he not been stupid enough to fly in an inadequate aircraft he would have been dictator of Spain in Franco's place. He might have been open to joining the Axis during WW2, with significant implications. Otherwise he would likely have died by the mid 1950s (he was born in 1872), with it being likely Spain would have become a democracy at least a decade earlier than OTL
Evan Durbin - one of the main Labour economic thinkers in the 30s and 40s and a really interesting figure. Personal assistant to Attlee during the war, he was elected M for Edmonton in 1945 and PPS to Chancellor Hugh Dalton from 1945-1947. Died rescuing his daughter from drowning on the Cornish coast in 1948, shortly before he was due to enter cabinet in a reshuffle. Had he lived he would have become a cabinet minister, might even have become Chancellor in Gaitskell's place in 1950 and potentially even leader. Either way he was destined to be one of the leading figures in the Labour Party in the 50s, instead he's a footnote no one has even been bothered to write a book about.
David Penhaligon - Liberal M for Truro 1974-86. A charismatic politician who's thick cornish accent was instantly recognisable. Was President of the Liberal Party from 1985-86, and Liberal-SDP alliance shadow chancellor from 1985. Killed in a car accident in December 1986. Had he lived would have been a very strong contender to become Liberal Democrat leader when David Steel retired
Hugh Gaitskell - Had he lived he would almost certainly have become PM in 1964 with a larger majority than Wilson in OTL.
John Smith - ditto to Gaitskell but 30 years later. Would have been an excellent PM.
Robin Cook - would have returned to cabinet when Brown became PM, maybe even as Deputy PM. He might even have been a plausible leadership candidate in 2010.
Harold Holt -
The Found Prime Minister: An Australian Politics wikibox tl | alternatehistory.com
Pompidou has been previously mentioned in this thread. He'd already made plans to run again in 1976, and would likely have won against Mitterrand.
Tony Crosland - had he lived he would have swapped jobs with Healey in the autumn of 1977 to become Chancellor. If Labour still lost office in 1979 he would have contested the leadership again. He was a less abrasive character than Healey so would have been less likely to rub MPs up the wrong way, which would have helped him in the 1980 leadership election, which he might well have won. Labour would probably still have lost the 1983 election, but there wouldn't have been an SDP breakaway and Labour would likely have returned to office in 1992.
Oliver Stanley - The de-facto tory shadow chancellor from 1945-50, would have been chancellor in the 1951 government had he lived. A very able politician, and perhaps a more plausible successor to Eden in 1957 than either Macmillan or Rab Butler.
Iain Macleod - Chancellor in the Heath government, died after one month in office before he could even deliver a budget. Had he lived Britain would have weathered the economic difficulties of the early 70s somewhat better. Macleod planned to serve 3 years as Chancellor then retire to the House of Lords, whether he would have or not we'll never know.
John Davies - Tory cabinet minister in the 70s and shadow foreign secretary under thatcher. Resigned from parliament when he discovered he had a brain tumour and died shortly afterwards. Would have been in the 1979 conservative government had he lived and been in better health.
Reginald Maudling - chancellor under Macmillan and douglas-Home, narrowly lost the conservative leadership to ted heath in 1965 and became home secretary in 1970. Resigned in 1972 due to ties to the corrupt architect John Poulson, became deeply depressed as a result and an alcoholic and died of cirrhosis aged 61. Had he avoided scandal would probably have been a contender to succeed heath as leader.