A few ideas (some of which are similar to things ones above, and somewhat agreeing with Contrarian's principles).
Modern Baseball
$70M Cap
All players 1947 or later
All pitchers with K/9 of 9.0 or above.
Alternatives, $90M cap, and add a rule that at most one pitcher has > 200 IP/162.
Stars and Scrubs
$80M Cap
At least $50M spent on stars - where a star has either $/PA > $10000, or $/IP > $40000.
At least one full-time player (>200 IP or >600 PA) is a superstar, either $/PA > $14000 or $/IP > $50000; play in park of superstar
Middle of the Century
$90M Cap
All players from the middle third of the 20th Century: 1934-1967
TV Stats Sequence
$100M Cap (though this is really variable)
No two players from the same year.
Every hitter must match the hitter chronologically before them in one of these three categories: Same AVG (to 3 decimal places), Same HR or Same RBI.
Every pitcher must match the pitcher chronologically before them in one of these three categories: Same Wins, Same Losses or Same ERA (to 2 decimal places)
Bad Pitchers
$110M Cap
Pitching staff must have given up at least 200HR and 600BB between them.
Every hitter must be a real-life teammate of a pitcher (same franchise and year)
OR
$80M Cap
Every pitcher must have a losing record
Every hitter must be a real-life teammate of a pitcher (same franchise and year)
New and Old
$120M Cap
No 20th Century players (i.e., 1900-1999)
At least $25M spent in each of these four categories
- 19th century hitting
- 19th century pitching
- 21st century hitting
- 21st century pitching