The C function getsockopt lets you get the error codes with the option SO_ERROR.
The possible error numbers are defined in the global errno.h. The relevant values are:

#define ETIMEDOUT   110 /* Connection timed out */
#define ECONNREFUSED    111 /* Connection refused */
#define EHOSTDOWN   112 /* Host is down */
#define EHOSTUNREACH    113 /* No route to host */
#define EALREADY    114 /* Operation already in progress */
#define EINPROGRESS 115 /* Operation now in progress */



//But here's the whole list on my Linux system (/usr/include/asm-generic/errno.h):

#ifndef _ASM_GENERIC_ERRNO_H
#define _ASM_GENERIC_ERRNO_H

#include <asm-generic/errno-base.h>

#define EDEADLK     35  /* Resource deadlock would occur */
#define ENAMETOOLONG    36  /* File name too long */
#define ENOLCK      37  /* No record locks available */
#define ENOSYS      38  /* Function not implemented */
#define ENOTEMPTY   39  /* Directory not empty */
#define ELOOP       40  /* Too many symbolic links encountered */
#define EWOULDBLOCK EAGAIN  /* Operation would block */
#define ENOMSG      42  /* No message of desired type */
#define EIDRM       43  /* Identifier removed */
#define ECHRNG      44  /* Channel number out of range */
#define EL2NSYNC    45  /* Level 2 not synchronized */
#define EL3HLT      46  /* Level 3 halted */
#define EL3RST      47  /* Level 3 reset */
#define ELNRNG      48  /* Link number out of range */
#define EUNATCH     49  /* Protocol driver not attached */
#define ENOCSI      50  /* No CSI structure available */
#define EL2HLT      51  /* Level 2 halted */
#define EBADE       52  /* Invalid exchange */
#define EBADR       53  /* Invalid request descriptor */
#define EXFULL      54  /* Exchange full */
#define ENOANO      55  /* No anode */
#define EBADRQC     56  /* Invalid request code */
#define EBADSLT     57  /* Invalid slot */

#define EDEADLOCK   EDEADLK

#define EBFONT      59  /* Bad font file format */
#define ENOSTR      60  /* Device not a stream */
#define ENODATA     61  /* No data available */
#define ETIME       62  /* Timer expired */
#define ENOSR       63  /* Out of streams resources */
#define ENONET      64  /* Machine is not on the network */
#define ENOPKG      65  /* Package not installed */
#define EREMOTE     66  /* Object is remote */
#define ENOLINK     67  /* Link has been severed */
#define EADV        68  /* Advertise error */
#define ESRMNT      69  /* Srmount error */
#define ECOMM       70  /* Communication error on send */
#define EPROTO      71  /* Protocol error */
#define EMULTIHOP   72  /* Multihop attempted */
#define EDOTDOT     73  /* RFS specific error */
#define EBADMSG     74  /* Not a data message */
#define EOVERFLOW   75  /* Value too large for defined data type */
#define ENOTUNIQ    76  /* Name not unique on network */
#define EBADFD      77  /* File descriptor in bad state */
#define EREMCHG     78  /* Remote address changed */
#define ELIBACC     79  /* Can not access a needed shared library */
#define ELIBBAD     80  /* Accessing a corrupted shared library */
#define ELIBSCN     81  /* .lib section in a.out corrupted */
#define ELIBMAX     82  /* Attempting to link in too many shared libraries */
#define ELIBEXEC    83  /* Cannot exec a shared library directly */
#define EILSEQ      84  /* Illegal byte sequence */
#define ERESTART    85  /* Interrupted system call should be restarted */
#define ESTRPIPE    86  /* Streams pipe error */
#define EUSERS      87  /* Too many users */
#define ENOTSOCK    88  /* Socket operation on non-socket */
#define EDESTADDRREQ    89  /* Destination address required */
#define EMSGSIZE    90  /* Message too long */
#define EPROTOTYPE  91  /* Protocol wrong type for socket */
#define ENOPROTOOPT 92  /* Protocol not available */
#define EPROTONOSUPPORT 93  /* Protocol not supported */
#define ESOCKTNOSUPPORT 94  /* Socket type not supported */
#define EOPNOTSUPP  95  /* Operation not supported on transport endpoint */
#define EPFNOSUPPORT    96  /* Protocol family not supported */
#define EAFNOSUPPORT    97  /* Address family not supported by protocol */
#define EADDRINUSE  98  /* Address already in use */
#define EADDRNOTAVAIL   99  /* Cannot assign requested address */
#define ENETDOWN    100 /* Network is down */
#define ENETUNREACH 101 /* Network is unreachable */
#define ENETRESET   102 /* Network dropped connection because of reset */
#define ECONNABORTED    103 /* Software caused connection abort */
#define ECONNRESET  104 /* Connection reset by peer */
#define ENOBUFS     105 /* No buffer space available */
#define EISCONN     106 /* Transport endpoint is already connected */
#define ENOTCONN    107 /* Transport endpoint is not connected */
#define ESHUTDOWN   108 /* Cannot send after transport endpoint shutdown */
#define ETOOMANYREFS    109 /* Too many references: cannot splice */
#define ETIMEDOUT   110 /* Connection timed out */
#define ECONNREFUSED    111 /* Connection refused */
#define EHOSTDOWN   112 /* Host is down */
#define EHOSTUNREACH    113 /* No route to host */
#define EALREADY    114 /* Operation already in progress */
#define EINPROGRESS 115 /* Operation now in progress */
#define ESTALE      116 /* Stale NFS file handle */
#define EUCLEAN     117 /* Structure needs cleaning */
#define ENOTNAM     118 /* Not a XENIX named type file */
#define ENAVAIL     119 /* No XENIX semaphores available */
#define EISNAM      120 /* Is a named type file */
#define EREMOTEIO   121 /* Remote I/O error */
#define EDQUOT      122 /* Quota exceeded */

#define ENOMEDIUM   123 /* No medium found */
#define EMEDIUMTYPE 124 /* Wrong medium type */
#define ECANCELED   125 /* Operation Canceled */
#define ENOKEY      126 /* Required key not available */
#define EKEYEXPIRED 127 /* Key has expired */
#define EKEYREVOKED 128 /* Key has been revoked */
#define EKEYREJECTED    129 /* Key was rejected by service */

/* for robust mutexes */
#define EOWNERDEAD  130 /* Owner died */
#define ENOTRECOVERABLE 131 /* State not recoverable */

#define ERFKILL     132 /* Operation not possible due to RF-kill */

#define EHWPOISON   133 /* Memory page has hardware error */

#endif

Source: http://www.xinotes.net/notes/note/1793/