Enrolling in your employer's 401(k) plan is a good start, but it's smart to consider alternate retirement savings accounts too, such as a Roth IRA, a traditional IRA and/or a health savings accounts (HSA). It might be worth directing some of your extra money towards one of those options.
Bonus points if you set up automatic contributions so your account continues to grow over time.
Caveats: While anyone can contribute to a traditional IRA, your income may disqualify you from the tax benefits. If you contribute to an employer-sponsored retirement plan and your income exceeds certain levels, the amount you can deduct may be limited. And if you're interested in contributing to an HSA, keep in mind that you have to have a high-deductible health care plan (HDHP).