Depends on what you consider a "rainy day." I don't know anyone that needs $100k for a rainy day.
The way I look at a rainy day fund is, what do I do if I suddenly lose my job? Others may need to look at their income stream in general, wherever it comes from (spouse, child support, etc.)
Most advice I hear is to keep about 6 months of living expenses in your emergency fund. This is just expenses, since in a true emergency you wouldn't be putting money into your 401k, etc. This is a rule of thumb--if you think you might have a harder time finding a job then save more.
This emergency fund money should be easily accessible. You don't want it tied up in long-term CDs if you need to access it in an emergency. It really isn't a good idea to put emergency money into the stock market (either directly or through a mutual fund).... look at 2009. You could lose half your money in a week, and what if the fallout from that crash causes you to lose your job too? So it's best to keep this money in short term, low-risk assets like cash, money markets or short term CDs. I know this blows because the fed has driven interest rates so low, it's punishing savers. But the alternative is to risk the possibility of needing government assistance if you lose your job.
Once you've put aside enough for your emergency fund, then you can take on some more risk. I still wouldn't put money I need within 4-5 years into the stock market (it's taken 4 years for the Dow to recover from March 2009). But if it's money not earmarked for something specific (buying a car or a house or kids tuition) then I like high-yield dividend paying stocks (except banks). Since we're talking taxable accounts here, dividends still (for now) get favorable tax treatment over capital gains. Just make sure you're selecting stable companies, or look for a high-yield divided mutual fund.
I'll also note that I'll never have $100k laying around (unless I get a huge promotion) because I max out my retirement savings accounts first, both a 401k and Roth IRA.
