Start of a series of posts taking a look at each power in Stargrave with an eye toward utility, combos, and other tricks. Many powers benefit in some way or another from specific loot items, but there are too many to mention. I will mention Ship Upgrades where relevant, since you have more control over getting them. Powers introduced in the supplements will be tagged as either (Q37) or (LP) as appropriate, with supplement-specific backgrounds similarly indicated.
Backgrounds: Biomorph, Fatewinder (LP)
Offers remarkable action efficiency for the user for two whole turns at the cost of serious strain and a high base activation number. Due to the rule that restricts models from using more than one Use Power action per turn, the primary effect is to let you use AS, make a power move, then take a second action to do something else. Removes the usually hard decision between using a power and trying to kill something or open loot counters. Could be used turn after turn to effectively grant 3" extra movement but you'll need healing to manage the strain. A move 7 model with AS could cover 17" running flat out, or 8.5" while hauling physical loot.
Handy mobility buffs that can be handed to anyone on the crew, but it doesn't directly increase speed. Vulnerable to being suddenly ended by Cancel Power, so be careful about committing to positioning that relies on the AP buff staying active - like hovering over lava in the Fire Moon scenario. If putting the buff on yourself, remember to take your power move after rolling so that you have the buff active if you succeed. Gets better the more obnoxious and/vertical terrain the table has on it.
Strong armor buff for the user at a high strain cost, one of the few ways to reach max 14 Armor without special gear. Text seems to suggest that powers used before a game that cause strain reduce your starting Health, which should probably be spelled out more clearly as a universal rule both for future proofing and for Mystic Trance combinations. Remember that if used pre-game you cannot exert to pass the activation roll but you won't suffer strain if you fail.
Either saves money on combat armor upkeep costs or hands out a small but meaningful damage buff on one basic shooting weapon. Versatile and handy power that gets twice as good with one of the ship upgrades. Slightly unclear whether the damage buff stacks with advanced weapons (or the gun from the weapons locker upgrade) that have a similar buff. As a pre-game power you only get one try to activate it and cannot exert yourself to pass.
Backgrounds: Investigator (LP), Rogue
Difficult, taxing, and unreliable power that seriously messes with loot haulers when it does actually manage to work. Can easily win games for you, but try not to get in situations where you need it to go off to avoid losing.
Beast Call (Q37)
Background: Hunter (Q37)
Difficult and moderately strenuous power that lets the user trigger an immediate roll on the Random Encounter table from the core book. Obviously intended to work in combination with the Control Animal power, but note that 45% of the results (including the most dangerous ones by far, the Warbots and Warphounds) on that chart aren't Animals. You do get to reroll the random location the creature(s) appear at if you dislike the first one, and you can't use this power again as long as the original summmons is on the table. Presumably some future supplement will offer variant Random Encounter tables to reflect different, less generic environments and hopefully they'll include mention of this power when that happens.
Medium strain power that lets you stop worrying about being unable to open a physical loot counter. The way the rules are worded won't let a friendly model immediately pick up the loot for free when you use this even if they're in position to - unless that friendly model is you. Even if you have better odds to conventionally open a loot counter you're in contact with, it may be worth using BL instead so you can grab the loot and immediately make a 1.5" power move. Every inch counts when you're dragging a crate around.
Background: Aristocrat (Q37), Rogue
Extremely difficult pre-game power that gives you a one use token with a strong but limited use. Cannot be stacked so you only get one token even if both captain and mate pass their roll on Bribe. Gains a strong benefit from one of the cheaper ship upgrades. Seems weak and very unreliable to me, although it would be a lot more palatable if the token could be used after a shooting roll rather than before.
Backgrounds: Biomorph, Cyborg, Hunter (Q37), Investigator (LP)
Incredibly strong defensive power for the user against most shooting that also messes with the creature AI rules. Comes with a high strain cost and unlike many buffs you lose it if you're stunned. Extremely nasty combo with Void Blade power, which could give you a cumulative +5 to Fight against many shots - but VB is also lost if you're stunned, so it's an all-or-nothing trick that would take time and strain to put back in place.
Incidentally, this is currently the power that's shared between the most different backgrounds.
Potent "counterspell" that lets you strip many buffs for a modest strain cost. Has the drawback of being useless if the enemy crew isn't using any of those buffs, which will happen when you run into "greedy" enemy officers that concentrate on Self-Only powers. Cannot remove most of the power buffs you'd most want to get rid of, but still pretty handy most of the time.
Background: Aristocrat (Q37), Fatewinder (LP), Veteran
Deceptively potent power that lets you activate a crew model in an officer phase on top of whatever ones you could normally activate with, and with a line of sight 24" range to boot. Useful for letting an isolated model act before soldier phase, which can help a backfield sniper get off a key shot or a loot hauler leg it for the table edge. The wording will even let you activate your first mate with this, although they wouldn't be able to activate nearby soldiers when they do so since they're acting in the "wrong" phase. Still a good way to get your mate to act before the enemy captain does, though. If the mate has Command itself, they could activate a soldier with it that way, letting six models go during your captain's phase.
Background: Aristocrat (Q37), Rogue
Close-combat power that lets you trade modest strain damage to take a strong point-blank shot that will shove and stun the target if it works. Good alternative to fighting when outnumbered or otherwise disadvantaged. Wording means that anything that affects shooting will apply to this attack for better or worse, so (for ex) your target would get +1 for a hasty shot if you moved into combat beforehand. It appears that you can't use a power move before using this power (since you wouldn't be in combat to even attempt to activate it) but you can certainly do so afterward if you hit your only foe. Quick-Step, another Rogue power, offers a more reliable but less aggressive way to avoid a bad melee situation.
Contacts (Q37, LP)
Background: Aristocrat (Q37), Investigator (LP)
Moderate difficulty out-of-game power that lets you select one piece of gear from any Advanced technology table (including the new ones in Q37 and LP) to purchase before the next game. This is going to let you cherry-pick whatever items you want as long as you have the credits to spend, although thankfully you can't select things from the Advanced Weapons or Alien Artifacts tables. If nothing else, this will keep you well-supplied with cheap consumables like Combat Drugs and Anti-gravity Patches as long as you can keep passing the activation roll.
Background: Hunter (Q37), Mystic
Rather situational power that lets you add an animal NPC as a temporary crewman in exchange for modest strain. Unusual in that it can be cancelled as a free action, so you could use it to grab an animal, move it somewhere problematic for your foes (eg into melee) then release it and grab another one. Obviously useless if there are no animals on the table (which is a good argument for taking the Beast Call power from Q37) but it's fairly good if there are lots of them to choose from. Beware of high-Will targets and things that look like animals but aren't, such as Warp Hounds. Also watch out for Cancel Power stripping your control at an inopportune moment. Newly-controlled animals will generally wind up moving in your soldier phase, or maybe your first mate phase if positioned right.
Backgrounds: Cyborg, Robotics Expert
Pretty much Control Animal except it works on robots instead, allows repeated Will checks to escape control, and has a slightly lower TN to resist. Utility is going to vary a lot based on how much your opponent likes robot soldiers in their crew, as NPC creature robots are rarer than animals and many of them are maddeningly immune to this power. This power is one of the major drawbacks to using robots, and people being afraid to use robots is one of the major drawbacks of this power. It's the circle of metagaming in action.