It's good for students to learn that multiplication is simply a faster form of addition. Once they see that relationship, multiplication will make more sense to them. Specifically, you can use a skip-counting game, where each person adds the factor to the previous answer and you go around the room to some specified product.
For Algebra teachers whose students are struggling with multiplication, you can add a variation that will connect this to linear equations: If you are working on 3's, the first time around, the first student starts with 0, the next student 3, then 6, 9, etc. until the first round ends. That's your times table for a factor of 3. The next round, the first student starts with 1, the next student will add 3 to get 4, 7, 10, etc. Third round starts with 2. Then, you can show them how this represented y=3x, y=3x+1, and y=3x+2.