[Wet Orange Ostrich Toilet]

Should humanity ever manage to colonize a large amount of planets, obviously there's going to be several factions (nations if you will) that will lay claim to their respective planets instead of one giant entity doing so. So there's bound to be some sort of border control for those citizens that want to go to planets that lie within a different faction's territory, just like today between different countries.

My question is, exactly how would it work with spaceships and such?

For the sake of simplicity, let's assume that the only way to move between star systems is over nodes, similar to Freespace.

[Scourge of Ages]

Probably like airports nowadays. You disembark, show your passport and give a reason you should be there (and you better have one, or else). But it would be on space stations, unless the ships themselves can make planetfall in your future.

And of course, there would always be your stowaways, coyotes, pirates, and other ways one could bypass that whole system and be somewhere they shouldn't. Unless every node was barricaded.

[Grizzly]

Considering that space colonization would be a very expensive effort initially I can easily see something like the Schengen Agreement but in space happening: The amount of people that is travelling is small enough and the nations doing space colonization themselves are few enough initially that a lot of governments would opt for an agreement that allows them to cut out the hassle entirely. In an optimistic future I tend to think that the notion of nation states gives out before we develop the means to do intergalactic travel easily.

This is however based on a very optimistic scenario: I can also see a future where any space colony would have a very strict cap on the amount of people that they can reasonably support in the first place due to the logistics of maintaning a steady oxygen supply. In such a scenario oppertunites for travel would be extremely limited, but in that case I agree with Scourge of Ages and think that the current system of visas and the like we have right now simply being transposed into space.

[Bobboau]

You are making inter-system control easy with that tech, as stated do your customs checks at the gates, and anyone who tries to get out of line gets their engines disabled.

Without that or with that and just looking at in-system, you just make an arbitrary line in space that if anyone crosses, you send out interceptors to blow them up/disable and board them. Unless they have a preapproved flightplan leading them through a customs check and then we are right back to the above situation. You will see these people coming a long time before they get anywhere near any of your systems so sending out a handful of interceptors would be trivial.

[Davros]

Then there would be illegal aliens

[Enioch]

Then there would be illegal aliens

I'm surprised it took this long for this joke to make an appearance. 

[Grizzly]

How did I miss that oppertunity? Well played Davros. My salute:

[Snarks]

Assuming there isn't any miracle scanning tech, we can extrapolate the process now except on an intergalactic scale. It would be incredibly ineffective. For intersteller trade to occur, then you cannot do any kind of indepth border control procedures at the jump nodes.

Modern border controls at busy ports are not very secured. Stowaways and contrabands regularly get across the border and pass by inspection. Now imagine if all the commercial traffic on Earth goes through a single port. The volume would simply be overwhelming.

Instead, I would suspect that border control takes place at secondary ports, the places that link the system with the associated planetary body, satellite, or space station, where the volume of traffic would be a lot less. This would leave room for smugglers/stowaways to hide in the space inbetween the jump node and ports, perhaps some hidden moon base or space station.