The most popular and recent one I can think of is Monero. They basically use the Cryptonite algo and due to the threat of ASICs and FGPA they had to fork to a slightly different algo about 2-3 times already. First it was the original Cryptonite algo, then Cryptonite V7, Cryptonite V8, and now its Cryptonite R. And from what I read they will change this algo every 6 months or so to defeat ASICS.
There are some smaller coins like Bitcoin Gold which switched from Equihash to a different variant of Equihash to make it mineable with GPUs but not with the ASICS which are all over ZEC.
So, a block so and so, the algo changes and miners adjust. Seems very simple so I wonder about complications.
I wonder about some coins getting stuck, maybe forever.
Yes there are complications. Whenever there is a forced algo change its usually against the majority of the hashpower interest. So the miner's with ASICs won't want to go with the fork which will change the algo. The only miners which want the fork are the GPU miners so they can make money again.
So when this happens its important that all the Services or Exchanges which use that coin update to the newest software with the fork. If they refuse then it creates issues. This happened in the past with Bitcoin. Where there was proposed block size increases but the consensus didn't agree.
The coins won't get stuck, they will just get stuck on the minority chain. You will still be able to claim them on the majority chain however.