If you're playing a game against opponents worth playing against (read: humans), building an Orkulus on a key choke point very early in the game (away from enemy frigate factories) can give you the decisive territory advantage. Although relatively common, using an Orkulus offensively by building it on an enemy's planet doesn't often work well in the early-game if the enemy is decent; they'll just build more ships and destroy it before it does much damage. Even if you have 2 Skirantras attempting to heal, that probably won't be enough against an opponent getting 30+ long range frigates. But the mere threat of building a starbase can also be significant; if you send a Migrator into a gravity well and send it to the other side of the enemy's frigate factories, the enemy might chase it with their entire fleet (allowing you to pursue and destroy ships), even if you never actually decide to deploy from that Migrator. If the enemy tries to chase it and your Migrator isn't in range immediately, the enemy will be losing a good amount of potential firepower while it chases.
An Orkulus on a choke point asteroid is extremely difficult for an enemy fleet to evade, and can be killer, in combination with a few Phase Jump Inhibitors.
The other starbases, which (obviously) can't move, are more difficult to use effectively, since an enemy fleet will simply move around it until it can engage well. Remember that TEC are especially good at tanking starbases, due to Ogrovs and due to LRM + Akkan Targeting Uplink (which outranges starbases). Still, static starbases provide a number of benefits: most importantly, they provide area defense around where it's placed - allowing you to put frigate factories and repair platforms there, making them somewhat difficult to destroy without the enemy taking significant casualties. Starbases give your fleet an area to regroup in, which is a very useful tactical option - without a starbase, when your fleet is outmatched and you're forced to retreat to a safe area further back, you will certainly lose control of the planet.
If the enemy is TEC and tries to attack your starbase by using LRM + Akkan, that gives you the ability to gain the fleet composition advantage by investing mostly in flak - your starbase needs to be durable enough to withstand a good number of shots though. (and if the enemy attempts to just bypass that planet, you may be in serious trouble if you don't have many standard damage-dealing units for scaring off capital ships)
A well-placed Argonev with the Red Button can destroy an entire enemy fleet at any stage in the game, if your opponent misjudges you or accidentally phases in on top of your starbase.
Putting an Argonev near the enemy's territory in an uncolonizable location they wouldn't be paying attention to can also give you a good opportunity to build and launch a surprise attack with Ogrovs/siege frigates (but if the enemy scouts you before you're ready, you're screwed).
