All ETFs tracking the S&P 500 Index I know (SPY, VOO, IVV) pay dividends several times per years. Is there any ETF that tracks the S&P 500 Index but instead of paying dividends they reinvest them automatically in stocks?
The problem there is that there's a tax due on that dividend. So, if you wish, you can buy the ETF and specify to reinvest dividends, but you'll have to pay a bit of tax on them, and keep track of your basis, if the account isn't a retirement account.
What you seem to want is a dividend reinvestment plan (DRIP). That's typically offered by the broker, not by the ETF itself. Essentially this is a discounted purchase of new shares when you're dividend comes out. As noted in the answer by JoeTaxpayer, you'll still need to pay tax on the dividend, but that probably won't be a big problem unless you've got a lot of dividends. You'll pay that out of some other funds when it's due. All DRIPs (not just for ETFs) have potential to complicate computation of your tax basis for eventual sale, so be aware of that. It doesn't have to be a show-stopper for you, but it's something to consider before you start. It's probably less of a problem now than it used to be since brokers now have to report your basis on the 1099-B in the year of sale, reducing your administrative burden (if you trust them to get it right).
Here's a list of brokerages that were offering this from a top-of-the-search-list article that I found online:
Some brokerages, including TD Ameritrade, Vanguard, Scottrade, Schwab and, to a lesser extent, Etrade, offer ETF DRIPs—no-cost dividend reinvestment programs. This is very helpful for busy clients. Other brokerages, such as Fidelity, leave ETF dividend reinvestment to their clients.
Presumably the list is not constant. I almost didn't included but I thought the wide availability (at least as of the time of the article's posting) was more interesting than any specific broker on it.
You'll want to do some research before you choose a broker to do this. Compare fees for sure, but also take into account other factors like how soon after the dividend they do the purchase (is it the ex-date, the pay date, or something else?). A quick search online should net you several decent articles with more information. I just searched on "ETF DRIP" to check it out.
A DRIP plan with the ETF does just that. It provides cash (the dividends you are paid) back to the fund manager who will accumulate all such reinvested dividends and proportionally buy more shares of stock in the ETF. Most ETFs will not do this without your approval, as the dividends are taxed to you (you must include them as income for that year if this is in a taxable account) and therefore you should have the say on where the dividends go.
Vanguard has low cost ETFs that track the S&P 500. The ticker is VOO, its expense ratio is 0.05%, which is pretty low compared to others in the market. Someone correct me if I'm wrong, but you won't have to pay tax on the dividends if it's in a retirement account such as a Traditional(pay taxes when you withdraw) or Roth IRA(pay income/federal/fica etc, but no taxes on withdrawal)...