This page from the CRA website details the types of investments you can hold in a TFSA.
You can hold individual shares, including ETFs, traded on any "designated stock exchange" in addition to the other types of investment you have listed. Here is a list of designated stock exchanges provided by the Department of Finance. As you can see, it includes pretty well every major stock exchange in the developed world.
If your bank's TFSA only offers "mutual funds, GICs and saving deposits" then you need to open a TFSA with a different bank or a stock broking company with an execution only service that offers TFSA accounts. Almost all of the big banks will do this. I use Scotia iTrade, HSBC Invest Direct, and TD, though my TFSA's are all with HSBC currently. You will simply provide them with details of your bank account in order to facilitate money transfers/TFSA contributions.
Since purchasing foreign shares involves changing your Canadian dollars into a foreign currency, one thing to watch out for when purchasing foreign shares is the potential for high foreign exchange spreads. They can be excessive in proportion to the investment being made. My experience is that HSBC offers by far the best spreads on FX, but you need to exchange a minimum of $10,000 in order to obtain a decent spread (typically between 0.25% and 0.5%). You may also wish to note that you can buy unhedged ETFs for the US and European markets on the Toronto exchange. This means you are paying next to nothing on the spread, though you obviously are still carrying the currency risk. For example, an unhedged S&P500 trades under the code ZSP (BMO unhedged) or XUS (iShares unhedged).
In addition, it is important to consider that commissions for trades on foreign markets may be much higher than those on a Canadian exchange. This is not always the case. HSBC charge me a flat rate of $6.88 for both Toronto and New York trades, but for London they would charge up to 0.5% depending on the size of the trade. Some foreign exchanges carry additional trading costs. For example, London has a 0.5% stamp duty on purchases.
One final thing worth mentioning is that, in my experience, holding US securities means that you will be required to register with the US tax authorities and with those US exchanges upon which you are trading. This just means fill out a number of different forms which will be provided by your stock broker. Exchange registrations can be done electronically, however US tax authority registration must be submitted in writing. Dividends you receive will be net of US withholding taxes. I am not aware of any capital gains reporting requirements to US authorities.