WillK has provided a great description of the Federal model and he is indeed correct in saying that many countries have done 'well' with such a system, although well is perhaps a matter of interpretation depending on your goals with such a model.
Two countries that come to mind that are Federal in nature are the USA and Australia.
I'm going to expand on Will's answer by providing some pros and cons from my experience in a Government context. Let's start with the benefits;
Because the states that join forces retain their own sovereignty (only giving up specific rights to the federal govt) it means that adding new states is a relatively simple exercise. In the case of the USA, they have literally 'bought' states and territories in the past, the most recent of which was Alaska (IIRC). If there is an existing province or state that wants to join the federation, in theory they are entitled to apply to join. Leaving? Well, like Will states that can be a cause of contention and attempts have led to civil war in the past. But, assimilating new territories is certainly a lot simpler.
Providing a defense force for a large country with a large population is more cost effective than trying to build a defense force for a small country, or worse yet, a large country with a small population. Also, certain states may be rich in minerals and the like, but not have strong agriculture. A federation allows different states to contribute to the wealth and prosperity of its citizens in different ways and provides for a domestic homogenisation of resources (state A's minerals get shipped around, as does state B's wheat, etc.) without the added complexity of diplomacy or currency issues. This concept easily expands to education, technical capability and other information services.
Different states may have different environmental constraints, belief systems, and needs from its neighbours. In a Federal environment, that state has the right to conduct some affairs in accordance with those needs. It's a flexible arrangement by virtue of the state still retaining at least part of its sovereignty. In the US for instance, each state can collect its own taxes, and run its own social welfare systems, etc. In Australia, they have a much broader remit because they have a restrictive constitution (everything at the federal level is prohibited unless the power is specifically granted in the Constitution) but in practice, this doesn't work because one thing that the states are specifically prohibited from doing is raising their own direct taxes.
There are (however) a few pitfalls...
It may seem like the USA and Australia have uniform codes of law and that they everyone in these countries is subject to the same rules, but that perception is very thin. In Australia for instance, every state as a separate criminal code and when something is being made illegal at the federal level, what's really happening in the background is the federal govt works with the state govts to get them to enact uniform laws in each state. This can be time consuming and very inefficient, especially if not all the states agree on the new law. What this means is that if you're the kind of dictator that wants to micro-manage your states, this model isn't for you.
Just because the federation of your states is a good deal, doesn't always mean that all your states are going to recognise that. The USA discovered that during the debate about slave ownership and the resulting Civil War. In Australia, there is discontent in some states who contribute significant mineral wealth to Australia but feel that they are short changed in terms of federal funding for services. Unless you have REALLY strong communication and good relations with all your states, this sense of being taken advantage of can build in certain regions without you noticing, especially if funds or other critical resources are being centrally redistributed.
On a Galactic Scale
Your ability to expand would be a big plus, especially if you treat every planet as its own state for the purposes of this model. The defense and redistribution of resources arguments make for great selling points, but the sheer scale you're talking about means that diversity almost forces fragmentation among the member states. Given that different planets are going to have different atmospheric, agricultural and mineral resource needs to begin with, this is only going to be exacerbated. Ultimately, the federation can thrive IF there is a strong unifying need among the member states, like defense.
But the one mistake you can make here is to try and micromanage the states in question. At the galactic scale, this federation becomes much looser and you're probably better off leaving most states to do their thing, only providing some principles to which 'their thing' must conform. Things like democracy, term limits, freedom of movement for all citizens, etc.
You won't achieve cultural homogenisation and that's actually a good thing. Most cultural practices tend to form around environmental necessities or conveniences; The British sailors (who came from cold climates) often mistook the minimal dress requirements of Polynesian people as a sign of a primitive culture rather than a natural reaction to a hot, humid climate.
What you hopefully will achieve is a political homogenisation; setting a minimum level of human (?) rights, how government is formed and how often it is replaced, freedom of movement, how it contributes to the welfare of the federation, and the rights it receives in resource distribution and defense in return.
If that's enough for you, then this can be an ideal form of government for states that have such distances between them. Given the political motivations you describe, you could almost think of each state as a franchise; they get to run things more or less how they see fit so long as they recognise a federal patron and conform to the rules that have been set for the broader federation.