My oldest card was opened around then as well (also BofA and with no rewards), but they eventually PC'd it to Cash Rewards automatically. Weird that they didn't for your card. Before cancelling I'd call them up and see if they'd be willing to PC to something else that may be more worthwhile for you. If nothing else, the Better Balance Rewards card is an easy $25 every three months just for purchasing a $1-2 item and immediately paying the balance.

Anyway, the general rule of thumb is to not cancel anything without an annual fee. However, if you do cancel a card, the history continues to be on your credit reports for ten years, helping to contribute to your average age of accounts (AAoA) and your report history. Since your oldest card is just a year older than the BofA card, I'm thinking that the bigger concern is the increase in total utilization that'll result from canceling. Any possibility of a CLI on one of your remaining cards?