How many times must I toss a coin in order that the odds are more than 100 to 1 that I get at least one head? How many times must I toss a coin in order that the odds are more than 100 to 1 that I get at least one head?
I believe that it is 10 times as if the coin is flipped ten times there is only ten outcomes that include only 1 head out of 1024 total outcomes. Is this correct?

Not quite. You want to compare getting at least one head to getting no heads at all; the probability of getting no heads at all during $k$ tosses is the same as getting all tails, i.e. $(1/2)^k$. The probability of getting at least one head is simply the complement of this, i.e. $1-(1/2)^k$. Thus you want $1-(1/2)^k$ to be at least 100 times greater than $(1/2)^k$. Thus we want 
$$
\frac{1-(1/2)^k}{(1/2)^k}=2^k-1>100;
$$
can you go from here?
