The following is a list of common strategies that will help improve your game. Some may be obvious, but their usefulness cannot be overstated.
Kiting as a Ranged Character
Kiting is the act of running from your enemies while dealing damage. In other games, kiting involves slowing your opponents so they cannot keep up with you. Many of the classes in Risk of Rain, however, move faster than most of the mobs in the game, making this unnecessary. Kiting works best for ranged characters.
Dealing damage while kiting differs from character to character, but the essential ideas remain the same. While running from mobs, a character should quickly turn in place to face his assailants and throw a few attacks at them when the character is a far enough distance away.
Keep in mind that a character can turn around in midair. This allows a character to jump while kiting, turn in midair, and fire before continuing to run. This is especially helpful on the Engineer character, as his Tri-nade attack will have a higher chance of hitting his oncoming targets.
Kiting as a Melee Character
While kiting best works with ranged classes, melee classes with invulnurability frames or a movement speed ability and point blank attacks can kite rather effectively. These include the Bandit's Smokebomb and Dynamite Toss; the Mercenary's Blinding Assault, Whirlwind, and Eviscerate; HAN-D's FORCED_REASSEMBLY and OVERCLOCK; and the Miner's Drill Charge, Backblast and To The Stars.
This method of kiting is a little counterintuitive. Instead of running away from the enemy mob, the character should run towards it. The character should then use their point blank attacks before using their movement ability to run away. This is best seen on a case by case basis.
Bandit:
The bandit should use their Smokebomb prior to combat and enter into the enemy mobs before using his Dynamite Toss. This will stun the mobs and allow the Bandit to make a hasty getaway. Keep in mind that successful Lights Out kills will allow him to repeat this process indefinitely.
Mercenary:
The Mercenary should charge into battle with Eviscerate and follow up with a Blinding Assault through the enemy. After the first Blinding Assault, he may use Whirlwind to deal additional damage before using Blinding Assault two more times through the enemy and finishing with an Eviscerate. This deals an incredible amount of damage, but if the enemy isn't dead, the mercenary can easily retreat. Note that if a truly hasty getaway is needed, the third Blinding Assault can be used away from the enemy to get a headstart on running.
HAN-D:
HAN-D's method is a little different as he can sustain himself fairly well using his DRONE ability. However, kiting can be necessary with a large number of powerful mobs. HAN-D should OVERCLOCK, run into the enemy mobs, and use FORCED_REASSEMBLY before laying on the HURT. Hitting the mobs with HURT after FORCED_REASSEMBLY will allow HAN-D more time in OVERCLOCK, which lets him keep his movement speed for running away.
Miner:
The Miner can easily charge up a Drill Charge to dash through a group of enemies, and then Backblast out of the group. This also leaves a window where damage can be output via To The Stars whilst the enemies are stunned, whilst still leaving the Miner out of range of their attacks. This tactic usually reduces enemies to quite low health, where they can be finished off with a Crush if they approach the Miner. When trying to escape a large crowd or powerful enemies, Backblast can be used to stun them, and a uncharged Drill Charge can be used to add extra distance.