If one has decided to make aliya, are there particularly good (or bad) times during the year to do so, beyond the desire to be there for chagim? Factors that seem relevant would include tax-related timing/deadlines, the school year, employment cycles (when is it easier/harder to get jobs), rental cycles (if leases are easier to get at certain times of the year), availability of government services for olim, and probably other factors I haven't thought of.
But as for the most common/popular times to come:
I am the research assistant (intern) on a study (currently unpublished) examining patterns of aliyah. (We sent the draft to the Ministry of Immigrant Absorption for feedback, and more data, but that's probably on hold for the next few months until after elections.) The hard data shows that avi's answer isn't totally correct.
By far, the most common time for aliyah is in the summer. Close to double the amount of people make aliyah during each summer month compared to each winter month. The reason for this is most likely as he said; it's easiest for families with kids to move outside of the school year. That's also when my family made aliyah.
The January 1st observation seems to be kind of arbitrary. Some years have it, some don't. Same with around the chagim (and Pesach).
But that's the worldwide data -- aliyah from all countries, both Western and not. What if we only look at American data?
Here, the summer spikes are much more pronounced. I would say maybe 5 times higher than during the winter.
Also, the January observation might seem to show up here -- see those December spikes? I would guess that because these are "rich Americans" making aliyah, and not say, desperate Russians, they can be more concerned about making it easier with taxes.
The idea about Pesach also shows up a little more here, but the difference is negligible. It might be reading too much into a blip on the graph.
I'm not going to post the graphs here, but current Russian aliyah does not show "summer spikes" anywhere near the American level. Clearly, it's an older population making aliyah. From France, there is a spike pattern, but it's also high the rest of the year, combing traits from both USA and Russia.
To summarize, right now is the best time of year to make aliyah.
But as for what is the most common time, it's definitely summer. From Western countries, January (for tax reasons) is also done by some; from third-world countries, it's more stable across the year.
From what I have seen there are 3 or 4 popular times to move to Israel.
-Right before or right after January 1st.
This is done mainly for tax purposes so that it is easier on your mind to remember when things are do for which country and you don't feel all confused. However this does not work well if you have children that need to enter the school system.
-A month or so before the Chagim (Rosh Hashana, Yom Kippur)
This is mostly done for religious reason as it just feels good. It is also good for children as the school year is just starting, and you can have a place for the children to go while you take care of all the things that need to be taken care of when you move.
-Right before Pesach
This is a time when Israel's weather is just about perfect, so moving heavy things or worrying about air conditioners and heaters is not so important. It aslo makes "cleaning for pesach" that much easier.
-The middle of the summer
Many families find that moving in the middle of the summer is best for the kids, as it seems like just one huge family vacation at first.
All Olim services and deadlines are based on the day you make Aliyah are not fixed to any yearly schedule. Except for specific laws that might be passed the year you make Aliyah, there is no real difference when you move. (For example, if they decide to change the import tax rates one year, that could be a factor... however that is very very rare.) As far as finding a Job, I have found that "hiring season" happens about once every 3-4 months depending on the industry.