The middle eastern peace process receives another setback, for starters.
After 1967, the Arabs were smarting from their defeat, and looking for a way to regain face. And the Yom Kippur war did that. The Arabs lost, but they managed to score some success against the much vaunted IDF. Among other things, that allowed Sadat to rebuild his support enough to make the Camp David accords possible.
No war means that the political scene remains unchanged, in the short term. The Arabs are going to still want their revenge, and possibly will continue to seek it on a conventional battlefield. Israel (and a lot of others) will continue to believe in the invincibility of the IDF. In short, neither side is going to go looking for peace. Another conflict somewhere down the line seems likely. A potential flashpoint would be the Lebanese civil war leading to a greater regional conflict, instead of limited fighting in Lebanon itself. Egypt remains opposed to Israel.
Military consequences will be interesting. For one thing, without the war we may see less awareness of the effectivness of Soviet SAMs and anti-tank missiles, and resulting lack of employment and/or countermeasures. The Israeli navy never get's its brief moment of glory, so it will be far reduced from its current position as a regional power. Israeli doctrine will remain unchanged, remaining a marriage of mobile armored thrusts and static defenses along the Golan and Suez defense lines.