short answer
Yes. LEGO says it sometimes offers double points on purchases, and you can earn a flat 20 points for each set you register. Surveys, quizzes and visiting the LEGO Facebook page also earn points, but LEGO does not publish how many. There is no fixed schedule for double points, so check LEGO.com.
LEGO Insiders (formerly LEGO VIP) members earn points mostly by buying LEGO. There are a few other ways to add to the balance, and a couple of rules that decide how many points an order actually earns.
LEGO's own help page says it "sometimes" offers double points on purchases. Which products qualify and when the promotion runs is announced on LEGO.com. I'm not listing typical months here because LEGO doesn't publish a schedule and the dates change from year to year.
A promotion usually covers selected products rather than the whole store, so check the product page before you buy. And points are always based on what you pay: if the order is discounted, you earn points on the discounted amount.
For a sense of the numbers: in the US you earn 6.5 points per $1, so a $100 order earns 650 points (exactly the US minimum for a $5 discount). During a double points promotion the same order would earn 1,300.
Register the sets you already own
Scan the QR code on the instructions and you earn a flat 20 points per set. It only works once per set, only for adults, and only for sets that have a QR code (most sets from about 2018 onwards). Full steps in How to register your LEGO set to earn points.
Surveys, quizzes and the LEGO Facebook page
LEGO's help page says you can earn points by taking part in surveys or quizzes, and that visiting the LEGO Facebook page also earns points. It doesn't say how many points either one gives, and offers change, so I've left numbers out.
What counts and what doesn't
Only LEGO.com and LEGO Stores earn points. LEGO Certified Stores (the ones with a yellow flag) don't, and neither do other retailers. Buying a gift card earns nothing, but paying with a gift card does. Points from a store purchase show up right away. For online or phone orders they arrive once the order has shipped and the payment has been taken.
Keep the points alive
Points expire if you go 18 months without earning or redeeming any. Registering a set or making a small purchase resets the timer. See How long are LEGO points valid?
See what your points are worth
Use the points calculator to turn a balance into dollars, pounds, euros, Canadian or Australian dollars, or read the LEGO Insiders points value guide.