Go here for some annotated games from a recent tournament I played in.
Here is a random assortment of problems. Click on the problem numbers for solutions. Some of my diagrams are currently acting up, but they will be fixed soon.
Problem 1:

Diagram 1

This classic study is by Richard Reti. White is to play and draw.
Problem 2:

Diagram 2

This problem appears in Edward Lasker's book Chess For Fun and Chess For Blood (or something along those lines). White is to play and mate in three. Despite the paucity of moves available, this problem is extremely difficult to solve.
Problem 3:

Diagram 3

Due to Erich Zepler, 1937. White plays and mates in five.
Problem 4:

Diagram 4

(White: Pe3, Pe7, Pf3, Pf6, Bd4, Bf5, Kh2, Rb6, Qb1.
Black: Pa6, Pb3, Pb2, Pd7, Pd6, Pg5, Nh8, Ba3, Be8, Ra2, Rg8, Kf7.)
Due to Gerald Anderson, 1944. White plays and mates in four.
Problem 5:

Diagram 5

I will get the info on the composer soon. This is what is known as a helpmate--Black moves first, and both sides attempt to get White to mate Black. The nice thing about helpmates is that you don't have to check any variations--you know your solution is right if it ends in mate. To counteract this, there are often many solutions to one problem (which is taboo in normal chess problems but encouraged with helpmates, especially if the solutions are related in some way).
Anyway, this is a helpmate in three (remember, Black moves first, and each side moves three times, with White's third move delivering checkmate). There are two solutions.
Problem 6:

Diagram 6

This is the famous "Saavedra Position." White to play and win.
Problem 7:

Diagram 7

Due to K. Watson. White to play and mate in two.
Problem 8:

Diagram 8

Due to Ernest Pogosyants. White to play and win.
Problem 9:

Diagram 9

This is a spectacular problem by Korolkov and Mitrofanov. White is to play and draw.
Problem 10:

Diagram 10

By the famous composer Oscar Blathy, who specialized in the ridiculous. White to play and win.
Problem 11:

Diagram 11

This is an extremely famous and brilliant composition by David Joseph. White to play and win.
Problem 12:

Diagram 12

(White: Pe3, Pe6, Pg2, Ph2, Nf4, Bd4, Rb8, Kc5.
Black: Pc4, Pf7, Pg6, Ph5, Bh6, Qc1, Kh4.)
Quoted in Kotov's classic book "Play Like a Grandmaster," this study is by A. Kazantsev. White to play and win.
Problem 13:

Diagram 13

Also quoted in Kotov's book, this study is by Korolkov, whom we have met already. White to play and win.
Problem 14:

Diagram 14

(White: Pb2, Pc2, Pg3, Na1, Nh3, Rb5, Re2, Kh5.
Black: Pa3, Pb7, Pb6, Pe3, Pf7, Ph7, Na8, Rc8, Bd8, Kh1.)
Sam Loyd liked to name his problems. This one is called "Excelsior," and it refers to a certain task which this problem accomplishes. That's all the hint you get. Mate in five.
Problem 15:

Diagram 15

One of Sam Loyd's most famous problems. It's called the "Steinitz Gambit." That's also a hint. Mate in three.
Problem 16:

Diagram 16

A miniature from Sam Loyd. Mate in three.
Problem 17:

Diagram 17

(White: Pd7, Nd3, Be2, Kf2, Qg1.
Black: Na7, Bc6, Kf7, Qf8.)
An incredible study by Alexander Seletsky. White to play and win.
Problem 18

Diagram 18

A study by Abram Gurvich. White to play and win.
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