Cruisers and Escorts play a very obvious role in STO; Cruisers are predominantly Tank/Healers while Escorts are primarily Damage/Debuff. Science ships, on the other hand, do not clearly fit into one category. Science ships have a variety of powers but you could classify them all as generally "Utility."
There are some powers that every science ship should have, in my opinion.
Reverse Shield Polarity - This is an Engineering ability that is widely regarded as the strongest ability in the game. Incoming energy weapons recharge your shields. It's just as awesome as it sounds.
Cannon: Rapid Fire - I suggest mounting turrets into every back slot on your ship and using CRF. The only exception might be if you're using a Deep Space Science Vessel, you might want to use Beam Arrays with Beam Overload.
Here's a rundown of my experience with various science abilities. I split them into these categories: Healing/Defense, Damage, Control and Debuff. Note that most of these are boosted by having a high Auxiliary.
Science Team - Absolutely necessary. Great shield heal, can be used against others, and clears Science debuffs like Viral Matrix.
Hazard Emitters - This is a hull heal over time, usable on yourself or others. It has a slightly shorter range than Science Team. It's a must-have for any science ship that wants to be a healer. It's a little underwhelming if you don't put skillpoints into it though, but there are consoles available for sale on Sol that boost your Hazard Emitters.
Transfer Shield Strength - Again, a must have for a healer. This is essentially the same thing as HE, but for shields. Same limitations and concerns as HE; put points into this and/or buy a console or you may feel underwhelmed.
Polarize Hull - Polarize Hull will decrease the amount of damage coming in and will make you immune to tractor beams. It's an extremely useful ability, especially since getting tractored can easily mean the end of you. It's a bit more useful in PvP, but every last bit of defense counts in Special Task Forces.
Tachyon Beam - Tachyon Beam damages your opponent's shields over time. It can be very powerful if you're spec'ed out in it and are running a high Aux. It's possible to have a very nice damage build by running high Aux, firing off a Tachyon Beam, then switching to high Weapons to finish the job. Note that having an EPS relay really helps. If I wasn't a support/healer science ship on Arak, I would have this build. Tachyon Beam serves to increase your overall DPS, so if you visualize it that way, you'll know when to use it; that is, there's no "proper" time to use it. You can open with it or close with it at will.
Charged Particle Burst - This ability damages your opponents within a 360 degree radius and disables cloaking devices. The damage is acceptable, but you can stack it to where it's pretty respectable. It's used mostly for its anti-cloak abilities, so this might be of interest to you if you're going to PvP. If you're strictly PvE, you may find that the damage just isn't worth it to justify taking this ability.
Feedback Pulse - One of my favorite abilities. When active, attackers will sustain damage when they hit you. This is great for adding to your DPS and, when combined with Reverse Shield Polarity, it can really annoy enemy Escorts. I would recommend taking this regardless of your build.
Gravity Well - Gravity Well makes a miniature black hole that sucks enemies toward it and does damage. The damage is not fantastic, although you can get it significantly higher by using consoles and skilling up in it. It has a variety of interesting uses, such as being a perfect trick to use against mines (might be good in the new episodes, which feature tons of dangerous mines) and slowing down enemy escorts. I'm divided on this power personally, but if you want to squeeze every last bit of damage out of your science ship, go for it.
Photonic Shock Wave - 360 degree knockback and does some damage. This is Kinetic damage, so it will be ineffective against a shielded target. I don't use it, but I can see some situations in which it might be helpful. For example, if you use the Tachyon Beam strategy above, you can fire off all your weapons and Shock Wave into your target.
Tractor Beam - This is a very simple ability that you will use in almost every fight. It allows you to hold the enemy where you want them to be, allowing you to unload everything into an exposed shield. It can also be used to stop a fleeing player in his tracks. I'd recommend this for anyone.
Tractor Beam Repulsors - This pushes everything away from you in a 360 degree radius. Very useful in some circumstances, especially if you need to escape. It's extremely effective against mines and will actually knock back gravity wells and tyken's rifts. It's not as necessary as Tractor Beam, but it's definitely something to consider. Keep in mind that in STO, energy weapons are less effective at longer ranges. If you find yourself crowded up with NPCs and you need some breathing room, Tractor Beam Repulsors will knock them away and you'll take less damage.
Mask Energy Signature - This is basically Cloak, but it sucks. It will hide you from view but you will be easily detectable and you get no damage bonus for coming out of MES. You also can't use it in combat. I would avoid this.
Scramble Sensors - This is one of the most useful Science abilities. It will cause enemy NPCs to attack each other (although it doesn't seem to work on some high level boss NPCs) and it will make players on the same team attackable to one another.
Jam Sensors - This will cause you to disappear off a single target's screen. Extremely useful ability, especially when you need to heal up. It's fairly short in duration and it can be cleared with Science Team but it means that you can shoot at them and they can't shoot at you. Definitely something to get and save for the right moment.
Viral Matrix - VM used to be overpowered, now it's a bit underwhelming. It disables three random systems except Shields. So it can take out weapons, engine, auxiliary, etc. It is useful but it's no longer necessary. I don't like the randomness of it, but it's still a useful ability to have and can give you the edge in a fight. It can be cleared using Science Team.
Energy Syphon - A very useful ability that is especially useful in PvP against Escorts (who likely will rely on having a high weapons power.) This is a great pick for a Damage build because it will boost your own power levels.
Tyken's Rift - Tyken's Rift drains power from all enemy ships within a certain radius. If you pump it up in terms of skills, you can pull power drains of around -20 from enemy ships. This can be pretty substantial.
That's a summary of all the space science abilities, complete with my experiences with them. I've used every single one in PvE and PvP. Most are useful in their own way, although I honestly can't find any reason to use Mask Energy Signature no matter what build you happen to use. It could serve some RP use if you want to RP that your ship has a cloaking device, but when it comes to combat, I just don't find it useful.
As you can see, Science ship debuff abilities seem to be the best out of the bunch, followed by healing and control. The damage abilities are not fantastic but if they're used correctly, it can seriously ruin a single opponent.
You'll also notice that Science abilities lend themselves toward combination maneuvers. Tractor Beam + Tachyon Beam + Shockwave + Tricobolt torpedo is one example. I'll do another post with these combos in a bit.