I find that it is tricky to know when to stop colonizing and give up on the rest of the worlds. Or simply pause and let your tax population grow. Colonies cost money (in the form of maintenance) to keep, so having too many colonies without a good income source will put great stress on your economy. Having high maintenance costs when you need to build warships or increase research is not a good spot to be in.

Also, having 100% morale will double your population growth. Early on, its easy to achieve this by reducing taxes to 0%. The expenses early on combined with a good 3000 bc starting amount might mean you can go for hundreds of turns without taxes before you need to change things. The numbers vary depending on how quickly you grow. Colonizing like mad might lead you to burn through this starting cash quite quickly. Ideally, you want a large enough tax population to be developed before you burn through the starting cash.

I'm good at these things, but I find the hard part is usually where you want to keep building more colony ships, even when its a bad idea.

----

Edit:
By being able to stop the colony rush early, I mean I think you should be ready for war by the time the colony rush ends. You should have a few star furies built (or a few dozen depending on the size of the map) and the tech for planet invasions researched before you run out of planets to colonize.

Nothing wrong with having a few spare colony ships kicking around, you can use them to move population to developing colonies.  Or upgrade them later on to transports.  It's colonising that will kill your economy with maintenance, colony ships (unless they have weapons on board) won't cost you any credits in maintenance per turn.

Winning at the colony rush is good, but once your economy is rolling you don't need to keep colonising like mad.  Spreading out wide means it takes longer for ships to travel from one edge of your empire to the other.  Which is fine, if you have an even distribution of ship building worlds, but otherwise it can mean you will be waiting many turns for reinforcements to arrive.

The colony rush seems to me to have three pulses.

First, all try to colonize those planets that they begin the game able to colonize.  Second, as extreme colonization gets researched, races begin to colonize those planets that they newly develop the ability to colonize.  Third, races go after the PQ1 planets that remain.

One very effective way to buy time to develop your empire and then shift to building a fleet is to get the other AIs into wars with each other.  Combine that with researching Trade early and selling it to every AI you can, and the AIs soon see you positively as they trade with you as they see other AIs negatively as they fight them.

They WILL get around to threatening and attacking you, but keeping each AI in two wars generally gains a LOT of time.

Borders are pushed by influence, and influence is mostly generated by population, racial stats and other factors such as starbases or buildings on planets.

So usually if you have some fully populated old worlds and newly colonized worlds some parsecs away, these corworlds will still dominate the influental zone until the new worlds are risen in population

One interesting way of defending is:

1.  Starbase fortifications.  They become stationary juggernauts + 

2.  Intensive farming!!!!! (For the population boost).   

3.  Mass colonies everywhere. 

The AI simply can't take over your colonies or destroy your starbases, in which case they can't hurt you.  To take over a single one of your 18 billion pop colonies would require like 4-6 troop transports, a tremendous expenditure of resources.  They just can't do it! Obviously this works best with super-breeder.  

In fact, they don't even try.  Despite having no military to speak of, none of the AI wishes to mess with me simply because they don't have the means to take over colonies.   

Re.member if they r not threatening there not ready to attack. What size is your map I like immence. Pirates don't happen often enough and there are not enough of them. The bigger the population the more money. What U research helps I like planetary improvements. I don't worry about scout ships. build like four factories per t planet what is your species starting out with market places help keeo your approval at %100 and your production at %100 don't be afraid to lower either later first the approval to 75% when U do this U will probably have to lower the other what U research is important u may have to trade U will have to have universal translater when U meet someone right now go for planetary improvements then work on your morale and economics the thalans have really good flat rate bonuses  U should trade for these I forgot put your best morale building on every planet only one will do if your income on the planet is more than the expense build laboratories as soon as U can trade for the treaties with all this properly done this should work U should be able to build a fleet when time will come build a crapload of colony ships also research sensor as soon as U can and build sensor ships and auto survey also the reason why your planets R in other peoples sectors is influence this is really not a problem unless your planet is about ready to rebell both influence structures and influence starbases can help alleviate this if U have enough planets this can be the other way around U should check out my basic stradegy guide