Splitting can be highly profitable if the player does it with the right cards. When splitting, never split tens or fives. (Tens refers to any card valued 10, whether it be the actual 10, or J, Q, K.).
However, always split aces and eights (despite of what the dealer is showing). Splitting aces should be obvious. With two eights (16), the player's only chance of winning is if the dealer busts. By splitting the eights, the chances of hitting two hands higher than 16 are quite good.
Other than aces and eights, the player's best bet is to split twos and threes against a dealer's 4, 5, or 6. The cards in the deck (4, 6, 7, 9), the rule is to split these cards only when the dealer's hand is showing a card of lesser value.
For a thorough guide to strategic splitting, refer to the blackjack strategy chart.
Note: All blackjack strategies discussed assume the blackjack rules found in the Introduction to Blackjack.