I've noticed that the various races tend to be way too weak, and you never really have to interfere with what's going on around the solar system. No one ever gets too strong that they start conquering all over the place. One race having terrible RCI values is more often then not a blessing. There simply never is a shift in the balance of power that forces you to change your strategy from simply getting two races to like each other enough to form the federation and then just invite everyone you can after that. You'll be left with no more then one or two non-federation members after that who won't be able to pose a serious threat anymore.
The events that I've seen happen in game so far really haven't had a huge effect on the solar system. A strong trend on the RCI values or a drop in planet condition really aren't going to affect how I play. Most of the time they do nothing but weaken races, which makes me less likely to need to interfere with them to either get them into the federation or prevent them from getting too powerful and creating either a fear empire or the solar axis pact. Diseases are the same.
I've been thinking about ways to make things more interesting, and I really think that some events that force you to change how you play for awhile are the way to go. These are either things that you either have to deal with or end up facing serious threats to your federation, or things that change the way you play for awhile. The point here isn't to make things harder for the player, but to make things more interesting for them.
Major events which push a race towards either joining an opposition alliance or conquering planets. Only a few of these can actually trigger in a given game, depending on difficulty level. None can happen once a race is in the federation:
-Low economy causes xenophobic sentiment. Basically the rise of the Third Reich for the Skylaxians, Andors, Evucks, or Acutians. You need to sooth them, deal with the dangerous leader, improve their economy, or get them in the federation. If you don't, they turn into a dangerous expansionist opposition faction with a big boost to economy and fleet production.
-Low economy or planet condition slowly turns the whole of the Boarines or Burlusts pirate. The number of pirate bases for that race rapidly increases unless you get them in the federation or improve their economy. If this happens too many times, the race will turn into a pirate empire.
-A special Peltian only disease that dramatically increases their aggression and ship production. Cured if they're in the federation.
-Warlust, the most militarily mighty race starts building ships like crazy and is much more likely to attack and conquer.
-Attractive target, a weak race is much more likely to be attacked and conquered by another race. Everyone but the Andors lose opinion with them every month, and their military power is greatly reduced.
-Joint attack, two races that really like each other attack a common foe. Improves both's ship production rate and they're unwilling to join or form the federation while the attack is going on. Increases the influence requirement to get them to form or join the federation if it succeeds, pushing them towards forming the Solar Axis Pact.
Events that make you need to change your playstyle for awhile:
-Anti-Hydral sentiment, lose 1 point of influence with the race every month for 20-40 months, you can't gain influence with this race while this is going on.
-Diplomatic dispute, two races are in a dispute over something like trade or territory. Any friendly action with one race hurts your influence with the other equally. The two races lose influence with each other every month.
-Increased/decreased independence, credit gains/losses with this race are halved while the event is active.
Other ideas to make the game more interesting and encourage different actions and playstyles:
-A means to upgrade your ship with the resources you collect, improving the effects for friendly/hostile actions like altering the RCI values of a planet or affecting the relations between races.
-Special bounty dispatch missions you can take from the Black Market that last a few months for more credits then the standard actions. These could be things like helping a government improve their environment or a pirate wanting you to capture a freighter for them. These are things that people are hiring any mercenary to do, so the other mercs will also try to complete these bounty board things too.