Does solo mining still exists in Bitcoin or other alt-coins?
Solo mining of Bitcoin would honestly require a serious setup, as well any setup would need continuous added infrastructure/hashpower as the difficulty of mining increases over time-- for any returns to be realistically expected within a "reasonable" timeframe. And that would be to find 1 block. Think 100s of TH minimum to even get lucky.
This is why even people who have setup large mining farms, say 50, or 100 miners, still rely on Pools where the combined hashpower of many miners together work towards solving the next block. This provides a more consistent return on investment and allows you to budget accordingly based on overall pool performance.
As far as Altcoins, new alts are relased all the time, solomining in a proof of work scheme becomes more difficult typically with higher network hashrates on that given coin. So its about getting in at the very very start. Usually difficulty jumps into the "pool now required" within minutes, or even faster. The more miners hashing, the harder it will be to solve a block before someone else does, because the entire network is searching to solve the same hash. The difficulty will adjust automatically in order to maintain the specified block time (different for each coin). So it's a fight basically, between the miners, and the network hash rate adjusts to keep "in time" say, 1 block per 10 minutes, etc.
Yes, you can solo mine alts. But truthfully, unless you are going to run a serious setup; including configuring your own stratum proxy server, mining on a pool and paying the 1 or 2% fee is really the way to go.