First, a clarification. No assets are immune to inflation, apart from inflation-indexed securities like TIPS or inflation-indexed gilts (well, if held to maturity, these are at least close). Inflation causes a decline in the future purchasing power of a given dollar1 amount, and it certainly doesn't just affect government bonds, either. Regardless of whether you hold equity, bonds, derivatives, etc., the real value of those assets is declining because of inflation, all else being equal.
For example, if I invest $100 in an asset that pays a 10% rate of return over the next year, and I sell my entire position at the end of the year, I have $110 in nominal terms. Inflation affects the real value of this asset regardless of its asset class because those $110 aren't worth as much in a year as they are today, assuming inflation is positive.
An easy way to incorporate inflation into your calculations of rate of return is to simply subtract the rate of inflation from your rate of return. Using the previous example with inflation of 3%, you could estimate that although the nominal value of your investment at the end of one year is $110, the real value is $100*(1 + 10% - 3%) = $107. In other words, you only gained $7 of purchasing power, even though you gained $10 in nominal terms.
This back-of-the-envelope calculation works for securities that don't pay fixed returns as well. Consider an example retirement portfolio. Say I make a one-time investment of $50,000 today in a portfolio that pays, on average, 8% annually. I plan to retire in 30 years, without making any further contributions (yes, this is an over-simplified example). I calculate that my portfolio will have a value of
50000 * (1 + 0.08)^30, or
$503,132. That looks like a nice amount, but how much is it really worth? I don't care how many dollars I have; I care about what I can buy with those dollars.
If I use the same rough estimate of the effect of inflation and use a
8% - 3% = 5% rate of return instead, I get an estimate of what I'll have at retirement, in today's dollars. That allows me to make an easy comparison to my current standard of living, and see if my portfolio is up to scratch. Repeating the calculation with 5% instead of 8% yields
50000 * (1 + 0.05)^30, or
$21,6097. As you can see, the amount is significantly different. If I'm accustomed to living off $50,000 a year now, my calculation that doesn't take inflation into account tells me that I'll have over 10 years of living expenses at retirement. The new calculation tells me I'll only have a little over 4 years.
Now that I've clarified the basics of inflation, I'll respond to the rest of the answer.
I want to know if I need to be making sure my investments span multiple currencies to protect against a single country's currency failing.
As others have pointed out, currency doesn't inflate; prices denominated in that currency inflate. Also, a currency failing is significantly different from a prices denominated in a currency inflating. If you're worried about prices inflating and decreasing the purchasing power of your dollars (which usually occurs in modern economies) then it's a good idea to look for investments and asset allocations that, over time, have outpaced the rate of inflation and that even with the effects of inflation, still give you a high enough rate of return to meet your investment goals in real, inflation-adjusted terms.
If you have legitimate reason to worry about your currency failing, perhaps because your country doesn't maintain stable monetary or fiscal policies, there are a few things you can do. First, define what you mean by "failing." Do you mean ceasing to exist, or simply falling in unit purchasing power because of inflation? If it's the latter, see the previous paragraph. If the former, investing in other currencies abroad may be a good idea. Questions about currencies actually failing are quite general, however, and (in my opinion) require significant economic analysis before deciding on a course of action/hedging.
I would ask the same question about my home's value against an inflated currency as well. Would it keep the same real value.
Your home may or may not keep the same real value over time. In some time periods, average home prices have risen at rates significantly higher than the rate of inflation, in which case on paper, their real value has increased. However, if you need to make substantial investments in your home to keep its price rising at the same rate as inflation, you may actually be losing money because your total investment is higher than what you paid for the house initially.
Of course, if you own your home and don't have plans to move, you may not be concerned if its value isn't keeping up with inflation at all times. You're deriving additional satisfaction/utility from it, mainly because it's a place for you to live, and you spend money maintaining it in order to maintain your physical standard of living, not just its price at some future sale date.
1) I use dollars as an example. This applies to all currencies.