For disc-based games, I pretty much expect them to be complete. I'll make exceptions for games I pick up really cheap or if I buy a lot. I grabbed a copy of Haunting Ground for $30 because it was missing the manual and I'm glad I did.

For carts, I used to collect almost exclusively complete games. I started out with NES and passed on games that were cart-only. But today, I wish I'd bought everything because I likely passed on games that have increased 10x in value since the early 2000's. Today I have what I think is an impressive collection of complete NES games, but at the same time I regret ignoring great games because they didn't come in a box.

Today I rarely pick up complete games because they've gotten so absurdly expensive and have switched to loose carts. Thankfully, I was able to get most of the complete games I really wanted during my complete only phase.