Wookiee Bowcaster
We honestly never found the bowcaster to be worth picking up. Although it has some neat features, such as a sniper zoom and the ability to bounce its bolts off of walls, these never quite got beyond the "gimmick" stage of appreciation for us. If you insist on using it, though, you'll find that it's only really effective when you hold down the fire button for a couple of seconds and let the weapon charge fully before releasing it to fire. If you do so, then you'll probably be able to get some one-shot kills on your enemies, and even if you miss, the bolt will bounce around until it hits something. Unfortunately, you'll only be able to fire off one of these bolts every couple of seconds, making this a pretty poor choice of weapon for intense firefights.
Concussion Rifle
The fearsome concussion rifle utilizes sonic energy to create large shockwaves at its target, resulting in explosions of sound that can heavily damage organic enemies caught in the blast. Most grunt-level enemies will be killed if they're anywhere near the blast when it goes off, making this an effective anti-infantry tool for you (and for the Trandoshan enemies that wield it). Again, though, it doesn't work very well against droids, and you do stand a good chance of being hurt by your own blast if you accidentally hit an obstacle in front of you or aim at something too close.
Grenades
Thermal Detonators: The most famous hand grenade in sci-fi mythology is a welcome backup weapon for your commando squadron. Although they aren't overweeningly powerful, thermals do a good job of clearing out packs of grunt-level enemies, like battle droids, Geonosian soldiers, and Trando slavers and mercs. Most of the organic enemies are smart enough to dive away from the grenade when it's thrown at their feet, but they'll usually take substantial splash damage from the blast anyway.
EC Grenades: EC grenades are going to be an absolute lifesaver when you're facing off against mechanized enemies. The electrical charge that they send out will drain any droid enemy of health over time, as well as stun them for a good period, with longer stuns being the reward for more accurate placement of the grenade. Although one grenade won't be enough to take down tougher foes like SBD's or droidekas, the stunning effect will usually last long enough for you to get up close and take down the target with blaster or sniper fire, or with your melee attack, if you're feeling adventurous.
EC grenades also work on organic enemies, but they won't do much damage; instead, they'll merely get the stunning effect for a short period of time.
Sonic Grenades: Sonic grenades are somewhat unique among the grenades in Republic Commando, in that they're not detonated according to a timer, but rather based on proximity, and due to the fact that they can stick to walls and the floor. When thrown, they'll either detonate immediately if they land near an enemy, or stay in one place until an enemy runs by, at which point they'll blow up. (They'll automatically self-destruct if no one comes in range within 15 seconds or so, though.) Just the fact that they immediately detonate when thrown at a target makes them more useful when used against biological enemies than thermal dets, but they do almost no damage to droids. Also note that their proximity trigger can be tripped by corpses, so if you're trying to lay one down where you suspect enemies might be moving, it will likely explode immediately if there are already fallen foes in the area.
Flashbangs: Although flashbangs don't do any damage themselves, they will temporarily stun any and all organic enemies that happen to see the bang when the grenade detonates; this effect will also temporarily muddle your vision if you happen to be looking at the blast, but it won't completely blind you, nor will it prevent you from moving as normal. (It will stun your teammates, though, so be careful where you throw it.) This is best used when dealing with an overwhelming number of organic enemies, such as Trandoshan slavers, since it'll let you sweep into their ranks unmolested and finish them off with your melee attacks. It can also work against singular powerful enemies, like the Trandoshan HAM, but has little effect on droids.