Yes they do.
I've seen it happening myself some months ago, while watching in two different monitors the BTC/USD, ETH/USD and LTC/USD prices.
I was watching Kraken (for 3 days), running the charts plus 3 indicators, and all the charts (plus the indicators) looked the same.
The only explanation was, that the majority of the transactions was made by bots, running the same parameters.
If someone else has a better explanation, feel free to express it.
Do they really? I often encounter this statement. And i have no idea as to why. This past few days, bitcoin is on the rise and most certainly than not altcoin's price surely follows. I am not saying this is bad but altcoins have very little in common with bitcoin. And they are certainly not carbon copies of bitcoin either. Why the heck is their price so closely connected despite being so fundamentally different?