You can call what you're asking about a 'wealth tax', or 'capital tax'.
These are taxes not based on income you earned in a year, but some measure of how much you own. Some countries (Italy I believe is a prime example) tax ownership of foreign land. Some countries tax amounts owned by corporations [Canada did this until ~5-10 years ago depending on province]. Some countries strictly tax your wealth above a certain level (Switzerland, as has been mentioned, does this).
One form of what you are referring to that does exist in the US is the 'Estate Tax'. This is a tax on the amount of wealth that a person owns, at the time they die. The threshold for when this tax applies has been very volatile over the last 20 years, but it is generally in the multi-millions, and I believe sits somewhere around $5M.
If these taxes start to crop up more and more (and I believe they will), don't be shocked at the initial 'sticker price'. Theoretically a wealth tax could replace some of the current income tax regime in many countries without creating a strict increased tax burden on their people. ie: if you owe $10k in income tax this year, but a $2k capital tax is instituted next year, then you are still in the same position as long as your income tax is reduced to $8k.
Whether these taxes are effective/preferable or not is really a question of economics, not personal finance, so I will not belabour that point.
Note: if the money you have saved earns money (interest, or dividends, or maybe rent from a condo you own), then those earnings are typically taxed alongside your wage income. Any 'wealth/capital tax' as I've described it above would be in addition to income tax on investment earnings.