Well to begin with, we'd better define invasion. From the OED:

invade enter (a country etc.), esp. in a hostile manner and with armed force with intent to control or subdue it; attack.

The second source I'd point to is the Wikipedia page for the List of invasions. While Wikipedia is a horrendous source for many disciplines, including history, it can be quite useful for this type of quantitative history.

Going straight from their list, the tally ends up like so:

 

No. of Invasions	Countries
8	USA.
6	China, Israel.
5	North Vietnam.
4	Vietnam.
3	France, India, Iraq, USSR.
2	Egypt, Indonesia, North Korea, Pakistan, South Korea, Syria.
1	Argentina, Biafra, Bulgaria, Cyprus, El Salvador, Greece, Hungary, Jordan, Morocco, Nigeria, Poland, Saudi Arabia, Somalia, Tanzania, Turkey, Uganda, United Kingdom.

 

So the basic face value answer is no, Israel has not committed the most invasions. The United States takes the No. 1 position with 8, beating Israel and China by 2. However, this is just a basic look at the statistics. And there are issues with these numbers too.

Firstly, how do we look at territories that changed their names or added to their countries during this period? North Vietnam conquered South Vietnam in 1976, becoming the united country called Vietnam. The new Vietnam added 4 invasions to its own tally, which if combined with North Vietnam would surpass all other nations on the list. Considering that the union of North and South Vietnam was not an equal one, but a conquest, and that those responsible for the invasions committed by North Vietnam were the same leaders during the later spate of invasions, I would argue that there is merit in counting the totals together. This would put

Secondly, the status of territories. Palestine is a notorious example. Looking at the list of invasions, I am certain some are not appearing there under Israel's tally, and that some may be missing too from their opponents in the wars that have occurred in that region since 1945. As well as that, there are contested territories which undoubtedly raise the issue of who is in control of land? I would suggest that France's invasions of Vietnam in 1945 and 1946 might not count at all as Vietnam was a French possession at the time, and that Vietnam had not truly thrown off the influence of France at this point

Thirdly, how do we count invasions that occur as part of one war? For example, Israel is give three invasions for the Six Day War in 1967, which was a simultaneous attack, and a part of one operation. But to take this as a measure of aggression would be wrong as the three nations were in alliance with each other. As well as this, /u/tayaravaknin points out that Israel was not the aggressor, yet by definiton, those were legitimate invasions.

Lastly on the issue of numbers, is the quality of Wikipedia as a source. As I said, it can be exceptionally useful, but it is also subject to the bias of those making edits. As they are not professionals, but volunteers(much like us here, in fact), they are more likely to be swayed by personal biases than a professional might be. As I pointed out above, I suspect several instances that would count as invasions may have been missed from the list. I'm not sure how the United States in Vietnam, for example, doesn't qualify at any point.

Finally, as an aside, I'd like to voice my disagreement with /u/tayaravaknin over this not "being history". It is a question about the military history of the world, and is wonderful for analysis, although I don't think I've quite done it justice here.

P.S. If you include the last twenty years, USA still comes out ahead of Israel by 1.

EDIT: Wow, tables look heaps cooler on here than on my test sub.

First of all, this question breaks the twenty year rule.

Second of all, Israel didn't exist until 1948, so I'm not sure how they could have invaded anyone, especially when it was they who were invaded in 1948.

Finally, I don't think your question can be answered without a legitimate discussion about what an invasion is. Is it aggressive, or does it also mean an attack in self-defense? Who decides?

In short, this question is too broad, breaks rules, and is missing a fundamental premise.

Thanks for the replies every one! Very interesting.