Feats are abilities characters can gain the represent something extraordinary. They could be from training, experiences, or just something beyond what characters can do.
Characters can choose to gain a Feat instead of an Ability Score Improvement, as noted in each class.

There are two official sources for Adventures League when it comes to Feats (DDAL legal):
Players Handbook (2014)
Xanathar’s Guide to Everything (2017)

Additional Sources

Expanded Racial Feats from D&D Beyond

Adds Racial Feats for the additional races (Genasi from Princes of the Apocalypse (2015), and races in Volo’s Guide to Monsters(2016))

Unearthed Arcana: Feats (2016)
Unearthed Arcana: Feats for Races (2017)
*Which is replaced by Xanathar’s Guide to Everything (2017)

Unearthed Arcana: Feats for Skills (2017 April)
*Geek & Sundry “OUR 5 FAVOURITE FEATS FROM THE NEWEST UNEARTHED ARCANA”
Brawny
Historian
Empathic
Theologian
Stealthy

*I would have preferred if the racial feats were all in Volo’s Guide to Monsters (2016), as it fits to have racial feats in a book with new races. I would have loved new general feats.
I’d also like the racial feats to have the specific requirements, and not just their racial requirement – as most feats\abilities are cultural rather than something genetic.
An example of this is Squat Nimbleness in Xanathar’s Guide to Everything (2017). It states “Dwarf or a Small race” so Dwarves, halflings, goblins…

Great All-Round Feats

Lucky

You have inexplicable luck that seems to kick in at just the right moment.

You have 3 luck points. Whenever you make an attack roll, an ability check, or a saving throw, you can spend one luck point to roll an additional d20. You can choose to spend one of your luck points after you roll the die, but before the outcome is determined. You choose which of the d20s is used for the attack roll, ability check, or saving throw.

You can also spend one luck point when an attack roll is made against you. Roll a d20, and then choose whether the attack uses the attacker’s roll or yours.

If more than one creature spends a luck point to influence the outcome of a roll, the points cancel each other out; no additional dice are rolled.

You regain your expended luck points when you finish a long rest.

Magic Initiate

Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You learn two cantrips of your choice from that class’s spell list.

In addition, choose one 1st-level spell from that same list. You learn that spell and can cast it at its lowest level. Once you cast it, you must finish a long rest before you can cast it again.

Your spellcasting ability for these spells depends on the class you chose: Charisma for bard, sorcerer, or warlock; Wisdom for cleric or druid; or Intelligence for wizard.

Suggested Spells for combat

Cantrips
Green-Flame Blade
Booming Blade
Eldritch Blast

1st Level Spells
Find Familiar
Hex
Shield
Goodberry

Best Feats for Combat

Great Weapon Master
Polearm Master
Sentinel
Sharpshooter
Shield Master
War Caster

* They are just listed here in alphabetical order. There are numerous sources to explain the feats and why they are so good.

Worst D&D5e Feats

1) Weapon Master

You have practiced extensively with a variety of weapons, gaining the following benefits:
Increase your Strength or Dexterity score by 1, to a maximum of 20.
You gain proficiency with four simple or martial weapons of your choice.

*Only conceivable use would be to become proficient in Firearms

Weapon Master Belk by Kang Jason

How to make it better

From DawnforgedCast

Weapon Master

You have practiced extensively with a variety of weapons, gaining the following benefits:

• Increase your Strength or Dexterity score by 1, to a maximum of 20.
• Choose 4 weapons. You add your proficiency bonus to damage rolls when you use those weapons.

2) Keen Mind

You have a mind that can track time, direction, and detail with uncanny precision. You gain the following benefits.

Increase your Intelligence score by 1, to a maximum of 20.
You always know which way is north.
You always know the number of hours left before the next sunrise or sunset.
You can accurately recall anything you have seen or heard within the past month.

How to make it better

From DawnforgedCast

Keen Mind

When you encounter an enemy you can draw upon your vast stores of knowledge to discern important details about their tactics and abilities. You gain the following benefits:

• Increase your Intelligence score by 1, to a maximum of 20.
• You always know which way is north.
• You always know the number of hours left before the next sunrise or sunset.
• You can accurately recall anything you have seen or heard within the past month.
• As a bonus action on your turn, make an Intelligence check:
  Arcana (Constructs, elementals, aberrations, shapechangers), History (dragons, giants, humanoids), Nature (beasts, monstrosities, plants), Religion (Undead, demons, devils).
  The DC check is equal to 8 + the Monster’s Challenge Rating. Advantage on the check if you’ve encountered the creature before, or spend time learning about and studying it. If you succeed you are able to determine the following traits of the monster:
  • Their immunities, resistances, and vulnerabilities
  • Their senses, languages, and any special abilities
  • Any Legendary or Lair Actions they may possess

This information can be conveyed to allies as part of the action. If you succeed on this knowledge check by 5 or more, until the end of your next turn, the party may add your proficiency bonus to all attack and damage rolls against that creature, as well as saving throws against any of its abilities.

*I made it a bonus action as a lot of DM’s would just let characters make the check, and many wouldn’t even count it as an action.

3) Linguist

You have studied languages and codes, gaining the following benefits:

• Increase your Intelligence score by 1, to a maximum of 20.
• You learn three languages of your choice.
• You can ably create written ciphers. Others can’t decipher a code you create unless you teach them, they succeed on an Intelligence check (DC equal to your Intelligence score + your proficiency bonus), or they use magic to decipher it.

*Would actually be better to just save downtime and use that to learn additional languages.

How to make it better

From DawnforgedCast

Linguist

You have studied languages and codes, gaining the following benefits:

• Increase your Intelligence score by 1, to a maximum of 20.
• You learn three languages of your choice.
• You can ably create written ciphers. Others can’t decipher a code you create unless you teach them, they succeed on an Intelligence check (DC equal to your Intelligence score + your proficiency bonus), or they use magic to decipher it.
• You gain advantage on Intelligence, Wisdom, and Charisma saving throws against any spells that are cast utilizing a vocal component in a language that you understand.

4-5) Durable & Tough

Durable

Hardy and resilient, you gain the following benefits:

• Increase your Constitution score by 1, to a maximum of 20.
• When you roll a Hit Die to regain hit points, the minimum number of hit points you regain equals twice your Constitution modifier (minimum of 2).

Tough

Your hit point maximum increases by an amount equal to twice your level when you gain this feat. Whenever you gain a level thereafter, your hit point maximum increases by an additional 2 hit points.

How to make it better

From DawnforgedCast

Tenacious

Hardy and resilient, you gain the following benefits:

• Increase your Constitution score by 1, to a maximum of 20.
• When you roll a Hit Die to regain hit points, the minimum number of hit points you regain equals twice your Constitution modifier (minimum of 2).
• Your hit point maximum increases by an amount equal to twice your level when you gain this feat. Whenever you gain a level thereafter, your hit point maximum increases by an additional 2 hit points.

6) Lightly/Moderately/Heavily Armored

Lightly Armored
Moderately Armored
Heavily Armored

You have trained to master the use of light/medium/heavy armor, gaining the following benefits:

• Increase your Strength score by 1, to a maximum of 20
• You gain proficiency with [the one type of] armor.

How to make it better

From DawnforgedCast

Armory Apprentice

You have trained to master the use of all armor, gaining the following benefits:

• Increase your Strength score by 1, to a maximum of 20
• You gain proficiency with all armors and shields
• You gain proficiency with four weapons of your choice

*Characters would still need to meet the Strength restrictions for Heavy Armour.

7) Actor

Skilled at mimicry and dramatics, you gain the following benefits:

• Increase your Charisma score by 1, to a maximum of 20.
• You have an advantage on Deception and Performance checks when trying to pass yourself off as a different person.
• You can mimic the speech of another person or the sounds made by other creatures. You must have heard the person speaking, or heard the creature make the sound, for at least 1 minute. A successful Insight check contested by your Deception check allows a listener to determine that the effect is faked.

*This ability is completely useless for anything other than faking to be someone else. And personally, the most successful salespeople I know have taken acting

How to make it better

Actor

Skilled at mimicry, dramatics, and performance you gain the following benefits:

• Increase your Charisma score by 1, to a maximum of 20
• You have an advantage on Deception and Performance checks.
• You can mimic the speech of another person or the sounds made by other creatures. You must have heard the person speaking, or heard the creature make the sound, for at least 1 minute. A successful Insight check contested by your Deception check allows a listener to determine that the effect is faked.

*As simple as removing the restrictions on when you get advantage when Deception and Performance can be used.

8) Dungeon Delver

Alert to the hidden traps and secret doors found in many dungeons, you gain the following benefits:

• You have advantage on Perception and Investigation checks made to detect the presence of secret doors.
• You have advantage on saving throws made to avoid or resist traps.
• You have resistance to the damage dealt by traps.
• You can search for traps while traveling at a normal pace, instead of a slow one.

*Only really beneficial if you’re doing a lot of dungeonering – so perhaps useful for Undermountain.

How to make it better

Dungeon Delver

Alert to the hidden traps and secret doors found in many dungeons, you gain the following benefits:

• You have advantage on Perception and Investigation checks made to detect the presence of secret doors and traps.
• You have advantage on saving throws and ability checks made to avoid or resist traps.
• You have resistance to the damage dealt by traps.
• You can search for traps and secret doors while traveling at a normal pace, instead of a slow one.
• You have advantage with Thieves Tools to unlock locked doors and disable traps.
• Well underground or in tight corridors (5′ wide), you can travel at a normal pace and move stealthily.

Sources

Featured Image: “Market Ambush” by Darren Tan. https://www.deviantart.com/wraithdt/art/Market-Ambush-81037854