This is a very broad question, but I'll do my best.
Technically, you can draw money out of your 401k at any time. However, be aware that if you withdraw money from your employer-sponsored retirement account before age 59.5, you may be subject to paying a 10% penalty for accessing your money early. Additionally, be aware that in a traditional 401k, the majority of the money in the account is likely to be pre-tax, meaning all withdrawn funds will likely be taxable as ordinary income. Thus, for many people under the age of 59.5, the 10% penalty and the tax bill can take quite a chunk out of the money you hope to withdraw.
Be aware that it is actually possible to take distributions from your 401k without a penalty as early as age 55, assuming you are fully retired from the employer sponsoring the 401k plan. However, this action may only be taken assuming the funds stay within the employer's plan. If the money in the account is rolled over to an IRA or a new employer's 401k plan, this is no longer an option. Of course, with this strategy the 10% penalty is avoided but the withdrawn funds are still likely to be fully taxable.
Lastly, another option available is to take what is known as 72(t) distributions, which enable people to access their 401k at any age without a penalty. In order to qualify for a 72(t) distribution, the employee must commit to taking substantially equal distributions from the retirement account every year for the longer of either five years or until you reach age 59.5. The amount of the distributions will be based on your life expectancy. The younger you are, the smaller your annual distributions must be. This strategy is most useful for someone who wants to retire early and must access money in an employee-sponsored retirement plan in order to bridge the gap between retirement and when other income (such as Social Security payments) will be available. As always, even though this strategy may enable a person to side-step the 10% penalty, the withdrawn funds will still likely be fully taxable.
I hope this helps.
Lon did an excellent job of reviewing your options. One thing I would add is that only certain plans allow you to withdraw funds at age 55, so you would need to check with the plan administrator.
I'll take a different approach here and say there is no age limit as long as you no longer work in any capacity for the prior employer for which you want to withdraw your money. Since you did not specify the situation, the other answers were good but did not provide an answer if this is the situation