Altcoins exist for many reasons – you can research why each exists by reading its white paper (a document that describes the coin and why it exists, plus what their plans are for the future).
If you check out
https://coinmarketcap.com/ you’ll see the market capitalization of hundreds of coins, so there’s obviously some interest in them.
>> I'd say it's equatable to a stock,
You’re right in that some people treat them as stock, hoping the value will rise over time.
>> Is it just a waiting game in hopes that a few eventually become widely accepted as currency?
Basically yes but it also depends on the cryptocurrency. For example, Ripple is not only a cryptocurrency but also a platform for inter-bank transfers so people are betting on the banks accepting Ripple for transfers.
You can find out more about each coin by clicking its name on
https://coinmarketcap.com/ and then clicking through to the website or announcement thread for background information.