Individual Retirement Accounts, both Roth and traditional, are tax-advantaged accounts with rules established by the Internal Revenue Service. The IRS does not enforce an IRA minimum; your IRA trustee, however, might.
The IRS sets annual IRA contribution caps that limit how much of a traditional IRA contribution you can deduct from your income, and how much you may contribute to a Roth IRA. The amount may be reduced if you are a high earner, or eliminated if your income falls outside the IRS' phase-out limits.
The IRS is only interested in making sure you do not put an excessive amount of your income into a tax-sheltered account. IRA trustees (the banks and brokerage firms that manage IRAs), on the other hand, want to make money. Therefore, many trustees require you to make a minimum deposit to open an IRA.
You can find discount brokers that have no IRA minimums; other firms have minimums of anywhere from $500 to $3,000 as of September 2010. In addition to account minimums, you should also look at per-transaction fees and other service charges. Some firms waive your annual account fee if you keep your balance above a certain threshold.