As far as the TEC starbase goes (and for most cases, Advent as well), it depends completely on whether you're up against AI's or humans.

The AI will mindless throw its army against your starbase, whereas a player is more likely to try to move around it without engaging it directly.  This fundamental difference in approach means that how you use your starbase is difference.  Against the AI it's a bulwark that stops their advance.  Putting it close to the edge of your gravity well (right where you expect them to warp in) and then covering your other flanks with mines is a great approach.  This is what the AI does most of the time. 

A player (at least a smart one) will look before he leaps, and is likely to go around rather than trying to go through your starbase.  You can't simply presume your starbase can block the enemy completely, so instead of treating it like an impervious barrier it's better to treat it like a speedbump, something the enemy fleet has to maneuver around if they want to get past it. 

Typically there are three positions I put my starbase: front-face, rear-facing, and planet-side.  A front-facing starbase is where I expect my enemy to warp in.  While a player will still move around this location, this means their angle of approach into the gravity well is quite predictable and I can place my defenses appropriately.  The second position is rear-facing.  This position is to try to prevent the enemy from going through this gravity well and into the next.  This method is designed to maximize the amount of time the enemy fleet has to use to get around your defensive line and into your next gravity well.  Using it combines a PJI or two with lots of static defense.  The final positioning I use is planet-side.  I typically do this when I need to protect my valuable civic structures in a gravity well I could lose.  By clumping all my defenses (including the starbase) into a tight ball, I can protect those civic structures and ensure their survival even if the planet is taken.

I find starbases are best placed in small gravity wells; neutrals and asteroids work great.  This is because there is a lot less room to maneuver and the starbases weapons can cover a lot more of the area of the gravity well.  This makes them harder to maneuver around and all the more powerful.  Choke points are obviously good places to put a starbase, and typically putting up some repair bays within range of it is also a great idea (starbases regenerate health notoriously slowly).

I personally believe the TEC starbase is the worst of the three, and the Advent is only better once it has its late-game meteor control upgrade.  The Vasari starbase is the only one I'd bother getting early or in considerable numbers.

Starbases are massive investments.  If you can afford to build starbases on all your planets, you're either obscenely rich or you're not spending your cash.  In the former case, you've already won the game, so why are you bothering putting up defenses in your back-end worlds?  In the latter case, you're sacrificing your fleet's strength, and a well planned enemy assault will break those starbases very easily.

As I said, a starbase is only a bulwark against an AI.  Against a player, it's a speedbump.  If you don't have a fleet that can compete with the enemy player, all the starbases in the world won't help you (cept maybe the Vasari one, but even then a significant volume of bombers will take it down).  Fleet first, starbases second.  You can get away with starbase spam against AI's because they throw themselves headfirst into their managerie of guns, but a player won't do this.  In fact, it's not uncommon to see a starbase killed by bombers or anti-structure frigates and never get to fire a single shot.

@ Darvin: You're assuming that everyone plays short games?  

In games that last half a dozen hours or more, a starbase is a tiny investment compared to even a decent sized fleet.

Of course it becomes a battle of attrition at this point (IMO, where the real strategy and war is at).

@ OP: I always place my starbases furthest away from phaselane I expect the enemy to come from since it buys time for my fleet to arrive. And if they choose to ignore it, fine by me, there'll be another starbase in the next system, similarly placed.

I tend to stick my starbases in choke points most of the time then dot the areas around the incoming phase lanes with mines. Thats where their most useful and in smaller wells as a previous poster said they can cover more of the gravwell and players will have a tough time getting their fleet around it without entering weopons range plus those mines should hopefully pick a few ships off as they jump in if a player doesnt be careful and scout (or delay them whilst they clear them before sending in a large fleet).

I also find them useful as a way of reinforcing wells that you just cant afford to let the opposing player take (like anyhting that wil get them a food hold in youre territory) just stick em next to the planet or at the phase lane they'll be coming in through and reinforce its firepower with a few upgraded guass cannons.

Obviously if the player decides to just skip around and move on that last one wouldnt really work but if they really want/need that gravwell they have to engage the starbase and thats when an upgraded starbase with guass cannon support becomes a real problem for an attacking player...well thats what I find most of the time anyway.

I like to stick TEC starbases out on the edge of a gravwell with big red button and a PJI nearby. Especially useful to put them near a path your opponent might take to go to your HW. Then when they get in range, bye bye fleet.

I prefer to use TEC starbases less as a weapons platform, and more as a huge, heavily armored, fighter base that has the ability to blow up half the enemies fleet with it. I rarely go for weapons or armor, and only if I have left over spots from my other upgrades and tons of spare money. I place it in the middle of a ball of defensive turrets and hanger bays, and let my fighters and bombers do the talking for me.