Some say to send customized connection requests.
In a small experiment I ran this week, I sent 150 new connection requests without a message and 150 with a message.
Results are in.
Connections accepted without a message: 53 (35%)
Connections accepted with a message: 57 (38%)
Bottom line: for increasing your network size, writing custom connection requests may not be worth your time.
However, sending custom requests may improve awareness and potential for engagement (e.g. clicking a link).