Full disclosure: EA gave me a digital copy of Star Wars: The Old Republic and 30 additional days of game time.
Make the character the focus
Instead of tossing a handful of profession-specific quests into the ocean of generic fetch and kill tasks that every player on a particular faction must drudge through, Star Wars: The Old Republic provides a lengthy and involved storyline for each class that stretches over the entire level range of that character. While some of these are admittedly better than others, they do succeed in making you feel like you are the focus of the game instead of just a bit player. It's almost like playing through eight more sequels to Star Wars: Knights of the Old Republic.
If that alone isn't enough to convince you, these long class quests also can have very different story-based outcomes at certain points based on choices you make throughout the process. In at least one instance, you can also have a companion character end up with a completely different personality based on some of the choices you make before recruiting her.
Better gear customization
While some games give you things like gem slots and appearance tabs, SW:TOR allows you to build your gear from scratch, using just about any graphic you like. First, you find an orange (this color on the name denotes that it's customizable) item of the appropriate tier that gives you the look you want. Then, you add armoring, mods, and enhancements to it until you have the exact mixture of statistics you want.
The level and quality of the add-ons (and not the base equipment) determines the armor and stat bonuses of the equipment, so if you find something you really like early on, you can wear it through most if the game if you choose by continually upgrading the components you apply to it.
Companion characters done right
Some MMOs have tried to add mercenaries or other tag-alongs in after the fact (and with varying amounts of success), but The Old Republic gives you this at release and does it better. Not only does each class get a diverse combination of races, personalities, and backgrounds, but you also get a mixture of combat roles that allow you to tackle different situations. If you're playing a tank, you may want a healer to accompany you. Sometimes you need to kill something fast, so you'll summon a damage dealer.
Even when you're playing solo, you're never alone, and towards the end of the game, you'll have your choice of several that you can swap out whenever you want. As a bonus, you can always send your active companion away to sell all the low-quality items you're carrying. It only takes one minute, and is a life (and money) saver when your inventory is full and you're two levels deep in the opposing faction's stronghold.
Your crew members also have independent affection ratings with you, and you can cultivate relationships (sometimes even romantic ones) with them. Each one has a different set of behaviors and gifts that they either like or don't like, and they can also present unique dialog options (or interrupt with comments) if they are present during certain parts of the story.
Crafting is not a timesink anymore
I absolutely love that I never have to stop questing and killing to craft items or gather resources. Since only one companion can fight alongside you at any time, you might as well find something for the others to do. SW:TOR allows you to send these inactive companions to gather raw materials or craft items.
Resource-gathering tasks do cost you a small amount of credits (in-game currency), but no longer must you spend your valuable gaming time trying to make your own items while standing in the middle of an action-free capital city. Now you just need to give them orders, wait for the timer to count down (while you're busy cleaving foes with your lightsaber), and the resources or finished goods just show up in your inventory no matter where you are.
Proper pacing of the content and leveling speed
One thing that I've never had to do while playing Star Wars: The Old Republic is grind for experience or money. BioWare has done an excellent job of pacing the content of the game. If you complete all of the quests on a given planet, not only will you experience a linked and cohesive plotline for that particular area, but you'll also be at the appropriate level to tackle the next zone. I never felt like I had to interrupt the flow of either my character's or tje game's story because I wasn't strong enough for the next area.
I've also always had enough money to purchase my new abilities (including the expensive speeder piloting skills) even after I foolishly spent money on low-level gear early on in my first character. Money (or lack thereof) was never an impediment like it was in many other MMOs.
If you decide that you've played through the Republic or the Empire's storylines enough, you can also choose to level your character through player versus player (PVP) action, space combat (flying your ship) missions, or repeatable flashpoints (dungeon-like instances.)