There are many different kinds of combinations in Mahjong, and the more difficult the combination is, the more points you win when you go out.  One way to think of this is how a royal flush is worth more than a pair ・similarly in mahjong, some hands are worth more than others.  Once you have mastered going out, you should aim to improve your hand so you can maximize the amount of points you can earn when going out.

I will now go into all of the combinations that exist in mahjong, dividing them up into straights, triplets, pairs, singles suits, inner numbers, and outer numbers.

-------------------------------
Straights
-------------------------------

All straights
A good hand to go for if you have no triplets.

 
1 Identical straight of same suit (1 point): e.g. 4,5,6 & 4,5,6 of balls

2 Identical straight of same suit (2 point)
 
Identical straight for all suits (1 point): e.g. 6,7,8 of each suit

 
1-9 of same suit (1 point)
 
 

===========
Triplets
===========
Triplet of any character tile (1 point)
As long as you have 1 triplet of any character tile, then you can go out even though there are no other combos in your hand.

 
All triplets (2 points)

3 non-stolen triplets

Identical triplet for all suits

================
3 4-of-a-kind
================

=========
Pairs
=========
All pairs (2 points)

==================================
Middle numbers only (1 point)
==================================
A hand that has only 2-8 tiles and NO character tiles. If all of your 1s and 9s are useless (i.e. they aren't part of a pair, straight, triplet, or 4-of-a-kind), get rid of them and go for this hand.

=======================
Single suits
=======================
Single suit & character tiles only (2 points)
If you have a lot of 1 suit and very little of the other suits, go for this hand.

 
Single suit & NO character tiles (5 points)

 
============
Exclusive
============
Outer numbers (1, 9) & character tiles (1 point)
Every set must contain a 1, 9, and/or character tile.

Outer numbers (1, 9) only (2 points)
Every set must contain a 1 and/or 9. No character tiles are allowed.

========
Other
========
Non-stolen (1 point)
If you are not close to any of the above, go for a non-stolen hand.

Closing your hand on 1st draw (2 points)
After the tiles have been distributed to everyone and your hand is coincidentally organized so that you only need 1 more piece to go out, you can earn 2 extra points if you can go out with that hand. You will need to announce this on your first draw so everyone is aware of this fact. Furthermore, you cannot alter your hand further and you must lie all your tiles face-down.

------------------
Random
------------------
Here are the points that are assigned by chance.
1. Self-pick (1 point): going out on a piece you drew.

2. Bonus tile(s) (1 point each)
Bonus tiles are determined by the tiles that are revealed in the center stack. The tile that follows the revealed tile is the bonus tile. For example, if the revealed piece is a 6 of balls, then the bonus tile is a 7 of balls. If the revealed piece is a 9 of sticks, the bonus tile will be a 1 of sticks. If a player goes out with a bonus tile, s/he will earn 1 point for each bonus tile s/he has.

3. Hidden bonus tile(s) (1 point each)
You will gain 1 point for each hidden bonus tile you have. Hidden bonus tiles can be revealed when a player goes out depending on the difficulty of the hand. Each combination reveals one bonus tile, and the bonus points that can be cashed in are determined by the total points those combinations are worth.

4. Going out on a 4-of-a-kind draw (1 point): If you go out on the piece you drew after revealing a 4-of-a-kind, you get one extra point.

5. Final piece (1 point): going out on the final piece drawn.

6. Final thrown away piece (1 point): going out on the final piece thrown away.

=============
E. Jackpots
=============
Any player who goes out with a jackpot hand automatically wins the game.

All wind tiles

Non-stolen all 3-of-a-kinds

Triplets of non-wind character tiles: white, green, red

All character tiles

Once-in-a-lifetime

All green

All 1 and/or 9

1 tile of each of the following: character tiles, and 1 and 9 of each suit

Going out on first draw
 

===================================
F. Advice regarding combinations:
===================================
Although you can win with nothing in your hand in poker, in mahjong, you must have at least 1 point in your hand.  Since there are many types of combinations that lead to points, in order to avoid confusion, when you first draw all your tiles, look at your hand for the following patterns:

-------------
Straights:
-------------
All straights: are you close to having all straights in your hand?
Identical straights: Are you close to having identical straights (e.g. 2,3,4 & 2,3,4)?
1-9: Are you close to having 1-9 of a single suit?

-------------
Triplets
-------------
All triplets: are you close to having all triplets in your hand?
Identical triplets: are you close to having identical triplets for each suit (e.g. (4,4,4) (4,4,4), (4,4,4))?
Character triplets: Are you close to having a triplet(s) of a character tile?

Pairs
Are you close to having ALL pairs in your hand?

Single suit
Are you close to having all of one suit (with the exception of character tiles)?

Inner numbers (2-8)
Is you hand close to having all inner numbers (2-8) and no character tiles?

Outer numbers (1 & 9)
Is your hand close to having all 1 & 9 in each of your sets (excluding character tiles)?

If you meet at least one of these conditions when you go out, you are guaranteed at least 1 point.  Expert players go out meeting multiple conditions, which is what you will be able to do if you play long enough.  If you want to become a good mahjong player, you should ask yourself these questions everytime you draw your hand.

The thing that is appealing about mahjong is that there are many possibilities.  Although you can win with nothing in poker, in mahjong, you must have some kind of combination, and you are rewarded based upon the difficulty of your hand.  The reason I love mahjong is because victory is based more on skill than luck and bluffing (e.g. poker).  But if you don't think winning with an awesome combination like a royal flush is worth more than winning by bluffing, then maybe mahjong isn't for you.