I'm going to give you a few basic boxing combinations but a majority of your favorite combinations will come from ones you've thought up. The key to thinking up a great combination comes from your understanding of how your body's weight and balance shift as you throw punches, what would be the proper punch to throw to compensate for that weight shift and what would punch would your opponent most likely throw during this.
The right combination will not only distract and startle your opponent, it will also protect you from counter punches that he/she throws. I've said this before and this is the perfect opportunity to restate it:
Power Tool Combo
Every punch you throw leaves you open for a counter shot!
This is boxing, not punching, so you don't want to be all marked and bruised up, you want to stay pretty! So, after throwing each punch in the combination, bring your hands back to their starting position so you will be covered up if your opponent decides to throw a punch in the middle of your combo.
When first throwing these combinations, throw them slow and focus on form and technique (using the tips I provided in the previous posts). The more and more you throw these punches slowly and properly, the quicker the muscle memory will build up and you will be able to throw these combos quicker and more effectively.
Remember: Force= Mass x Acceleration. So the faster you throw the punch, the greater the force, force=power!
I tell a lot of the new fighters who come into the gym to think of combinations as if they are salsa dancing and/or as one of those inflatable punching bags you had as a kid. I say salsa dancing because in order to throw the punches quickly and effectively, you have to keep your hips nice and loose and let them move freely. I mention those inflatable punching bags because if you remember, whenever you'd punch it, it would spring right back. You have to do the same with boxing, if you rock back, comeback quickly with a punch. If you sway left, come back to center with a quick punch and so-on.
Basic Boxing Combinations
Use this key for the punches:
Jab Cross(right) Hook (head) Left Uppercut Right Uppercut Hook (body)
Remember these punch numbers because this is what I will be using for now on!
1-1-2: Using the jab to advance you will quickly throw it out twice to hinder your opponents vision and then throw your powerful cross behind it. 1-(1)-2-3: You can either chose to throw the jab twice or once. After you throw the cross, you'll be in position, since your weight will be shifted to your left (southpaw fighters to the right), to throw the hook from there. 2-3-2: This punch combination has to be thrown very quickly and done when your opponent isn't expecting it. I like to throw it when I can tell he is either off balanced or is tired. Once again, focusing on balance and hip movement will add speed to this combination. 1-5-3-2: This Jab-Right Uppercut-Hook-Cross combo is a deadly combo to throw against an opponent who you notice is leaving his "chin out." That means that in his stance, his head is extended past his lead knee or foot, leaving his jaw vulnerable.