As Oded has stated, some badges are too resource-intensive already to award. Tracking them would only cause much more unnecessary load.
Others may not be tracked because they are obsolete (e.g. Precognitive/Beta, Analytical).
These are the currently untrackable badges.
(m indicates a badge that can be awarded multiple times.)
Question Badges
(Silver) Favourite Question: Question favorited by 25 users. m
(Gold) Stellar Question: Question favorited by 100 users. m
(Bronze) Nice Question: Question score of 10 or more. m
(Silver) Good Question: Question score of 25 or more. m
(Gold) Great Question: Question score of 100 or more. m
(Bronze) Popular Question: Question with 1000 or more views. m
(Silver) Notable Question: Question with 2500 or more views. m
(Gold) Famous Question: Question with 10000 or more views. m
Answer Badges
(Silver) Enlightened: First to answer and accepted with score of 10 or more. m
(Silver) Generalist: Provide non-wiki answers of 15 total score in 20 of top 40 tags.
(Silver) Guru: Accepted answer and score of 40 or more. m
(Silver) Lifejacket: Answer score of 5 or more to a question score of -2 or less that goes on to receive a score of 2 or more. m
(Gold) Lifeboat: Answer score of 20 or more to a question score of -3 or less that goes on to receive a score of 3 or more. m
(Bronze) Nice Answer: Answer score of 10 or more. m
(Silver) Good Answer: Answer score of 25 or more. m
(Gold) Great Answer: Answer score of 100 or more. m
(Gold) Populist: Highest scoring answer that outscored an accepted answer with score of more than 10 by more than 2x. m
(Silver) Tenacious: Zero score accepted answers: more than 5 and 20% of total.
(Gold) Unsung Hero: Zero score accepted answers: more than 10 and 25% of total.
Participation Badges
(Silver) Pundit: Leave 10 comments with score of 5 or more.
(Bronze) Precognitive: Followed the Area 51 proposal for this site before it entered the commitment phase.
(Bronze) Talkative: Post 10 messages, with 1 or more starred, in chat.
(Silver) Outspoken: Post 10 messages in chat starred by 10 different users.
(Silver) Yearling: Active member for a year, earning at least 200 reputation. m
Moderation Badges
(Gold) Constable: Served as a pro-tem moderator for at least 1 year or through site graduation.
(Gold) Sheriff: Served as an elected moderator for at least 1 year.
(Silver) Reviewer: Complete at least 250 review tasks. This badge is awarded once per review queue
(Gold) Steward: Complete at least 1,000 review tasks. This badge is awarded once per review queue
[Note: Reviewer and Steward can be tracked from the review queue itself.]
(Bronze) Synonymizer: First approved tag synonym.
(Silver) Taxonomist: Create a tag used by 50 questions.
Other Badges
(Bronze) Announcer: Share a link to a question later visited by 25 unique IP addresses. m
(Silver) Booster: Share a link to a question later visited by 300 unique IP addresses. m
(Gold) Publicist: Share a link to a question later visited by 1000 unique IP addresses. m
Tag Badges
One can track Tag Badges by switching the 'Next Privilege' menu to a 'Track next Tag Badge' menu.