As I've been running my homebrew games, I've found the need to create a few more feats to accommodate builds and characters that my players (or I) have been interested in.

Agile Defense

• Gain 1 Dexterity
• While you are not using a shield or heavy armor, and have at least one hand free, gain the following advantages:
  • Advantage on any Dexterity (Acrobatics) check made to avoid a grapple or shove attempt. This does not aid you in attempts to escape a grapple.
  • +2 AC against non-spell attacks.

This allows a Monk to function reasonably well as a Defender-style character, without a shield (which is both awkward to become proficient in, and anti-thematic); Monks normally lack sufficient mitigation to function in that role until later in the game. This feat is carefully kept comparable to the similar Moderately Armored feat - the AC bonus is intentionally inferior to a shield and non-stackable, while the defense against grapple/shove is solid and thematic, but a bit niche.

Combat Training

• You gain proficiency with one weapon of your choice.
• When you take the Attack action, you may choose to gain advantage on all attacks until the end of your turn. You may not use this ability again until you have taken a long rest.
• Choose one of the following fighting styles:
  • Defense: Increase your AC by 1.
  • Great Weapon Fighting: When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll. The weapon must have the two-handed or versatile property for you to gain this benefit.
  • Archery: Gain a +2 bonus to attack rolls you make with ranged weapons.
  • Dueling: When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon.

This feat is intended to add a little versatility that is already available by taking one level of Fighter. I don't like the way a dipped level throws off the power curve; the game is balanced/structured around power leaps at specific levels, and a Fighter-1/Sorcerer-4 (for example) is very weak for a level 5 character. In particular, archer-style builds make the Archery fighting style effectively mandatory, forcing many interesting ranged builds to dip fighter.

Lancer

While riding a friendly creature at least one size larger than yourself, gain the following benefits:

• You may use your bonus action to prompt your mount to Dash.
• If you take the Attack action on your turn, you can use a bonus action to perform one Shove using your mount.
• You are proficient with lances, and have +1 on attacks with lances.

One of my players really wants to actually play the old mounted-gnome-on-a-dog character, which isn't really viable in 5e. This feat attempts to make mounted combat a straightforward proposition, and to make a character based around that concept a functional skirmisher/striker. I'm a fan of feats that allow good bonus-action-economy, and since mounted combat doesn't really rhyme with polearms, crossbows, or two-weapon fighting, it seems like a good enabler.

A few changes to existing feats

I also am irritated by pointless restrictions that I find in a few current feats. Here are a few changes:

• Grappler additionally allows you attempt to grapple creatures one size larger than you would normally be able to. This seems like the clear intent of the original (un-errata'd) feat language, and make the feat much less niche.
• Crossbow Mastery allows the bonus attack action with a shortbow as well as a hand-crossbow.
• Heavy Armor Master reduces the damage it affects by your character level, rather than by three, but is limited to removal of at most half of the received damage, and also affects magical damage of those types and force damage. This feat was very strong at low levels, but became pointless rapidly - the change allows it to scale with your level, and to affect damage types that you will actually continue to receive at higher levels.
• Keen Mind additionally grants advantage on any Intelligence check to recall information which they may have encountered previously, which includes the majority of History/Religion/Nature/Arcana checks. This makes the feat matter at all.
• Linguist additionally allows you to recognize what language is spoken or written, even if you do not know it; and given 1 hour of effort during a long or short rest, you can roughly translate a short passage from any language you do not know into common.
• Martial Adept grants two d6 superiority dice, and an additional die at levels 5, 11, and 17. (one die made this feat so underwhelming that I've never seen anyone take it).
• Weapon Master additionally grants: when you roll a 1 on an attack roll using any of the four chosen weapons, you may reroll the die, and must use the new roll.