No.
A salary cap would introduce more problems than address those it would purport to "solve", and does more to make great teams mediocre than it does bring poor teams upward.
2008 playoff teams and ranking (among 30) of season payroll:
4. Red Sox
5. Cubs
6. Angels
7. Dodgers
8. White Sox
12. Phillies
15. Brewers
(25. Twins, who lost a playoff game to the White Sox)
29. Rays
The top three payrolls missed out.
What about 2007?
1. Yankees
2. Red Sox
4. Angels
8. Cubs
13. Phillies
23. Indians
(24. Padres, who lost a playoff game to the Rockies)
25. Rockies
26. Diamondbacks
OK, the top two are here, but there sure are a lot of budget-minded teams as well.
Finally, take a look at champions in the NBA and NFL for the last 20, 30 years. There's a lot of repeaters, and the trophies don't get passed around a lot. That's not the case in baseball.