My 6 year old loves takenoko... I also love it! It's a very pretty board game with nice pieces and art work and not too expensive. This would be my number one choice for this age!
He can give a relatively good game of catan, although he needs help picking spots and a bit with card management.
He tries at ticket to ride, but it's a bit beyond him planning his routes. His big sister though could do it when she was 7, but approaching 8, rather than only just 7.
For fun, if you have a few players... I love one night ultimate werewolf. Not a board game really and very silly but has us in hysterics and my 4 year old can play it. Also only takes a few minutes to play.
We have Scotland Yard as mentioned by another poster, you work as a team and a single player. So as long as someone capable is the single player and the 7 year old is on the team, that can work.
This thread has inspired me to dig out carcassonne (not played in years) and play it with the kids.
I love board games, and I have lots of very complicated strategic type ones that I play with dh. I cannot stand monopoly, so I train them up from quite an early age, to play board games I enjoy 