Runes are now (August 1999) finally included in Unicode (from the version 3.0 onward). They are located in block 16A0-16FF, between Ogham and Khmer scripts.

Here's a sample from http://www.unicode.org/Public/UNIDATA/UnicodeData.txt
(also available as my local copy http://www.megabaud.fi/~karttu/Runes/ftp://ftp.unicode.org/Public/UNIDATA/UnicodeData-Latest.txt which, however, might not be the most recent version there is.)

@@      16A0    Runic   16FF
@               Letters
16A0    RUNIC LETTER FEHU FEOH FE F
16A1    RUNIC LETTER V
16A2    RUNIC LETTER URUZ UR U
16A3    RUNIC LETTER YR
16A4    RUNIC LETTER Y
16A5    RUNIC LETTER W
16A6    RUNIC LETTER THURISAZ THURS THORN
        x (latin small letter thorn - 00FE)
16A7    RUNIC LETTER ETH
16A8    RUNIC LETTER ANSUZ A
16A9    RUNIC LETTER OS O
16AA    RUNIC LETTER AC A
16AB    RUNIC LETTER AESC
16AC    RUNIC LETTER LONG-BRANCH-OSS O
16AD    RUNIC LETTER SHORT-TWIG-OSS O
16AE    RUNIC LETTER O
16AF    RUNIC LETTER OE
16B0    RUNIC LETTER ON
16B1    RUNIC LETTER RAIDO RAD REID R
16B2    RUNIC LETTER KAUNA
16B3    RUNIC LETTER CEN
16B4    RUNIC LETTER KAUN K
16B5    RUNIC LETTER G
16B6    RUNIC LETTER ENG
16B7    RUNIC LETTER GEBO GYFU G
16B8    RUNIC LETTER GAR
16B9    RUNIC LETTER WUNJO WYNN W
        x (latin letter wynn - 01BF)
16BA    RUNIC LETTER HAGLAZ H
16BB    RUNIC LETTER HAEGL H
16BC    RUNIC LETTER LONG-BRANCH-HAGALL H
16BD    RUNIC LETTER SHORT-TWIG-HAGALL H
16BE    RUNIC LETTER NAUDIZ NYD NAUD N
16BF    RUNIC LETTER SHORT-TWIG-NAUD N
16C0    RUNIC LETTER DOTTED-N
16C1    RUNIC LETTER ISAZ IS ISS I
16C2    RUNIC LETTER E
16C3    RUNIC LETTER JERAN J
16C4    RUNIC LETTER GER
16C5    RUNIC LETTER LONG-BRANCH-AR AE
16C6    RUNIC LETTER SHORT-TWIG-AR A
16C7    RUNIC LETTER IWAZ EOH
16C8    RUNIC LETTER PERTHO PEORTH P
16C9    RUNIC LETTER ALGIZ EOLHX
16CA    RUNIC LETTER SOWILO S
16CB    RUNIC LETTER SIGEL LONG-BRANCH-SOL S
16CC    RUNIC LETTER SHORT-TWIG-SOL S
16CD    RUNIC LETTER C
16CE    RUNIC LETTER Z
16CF    RUNIC LETTER TIWAZ TIR TYR T
16D0    RUNIC LETTER SHORT-TWIG-TYR T
16D1    RUNIC LETTER D
16D2    RUNIC LETTER BERKANAN BEORC BJARKAN B
16D3    RUNIC LETTER SHORT-TWIG-BJARKAN B
16D4    RUNIC LETTER DOTTED-P
16D5    RUNIC LETTER OPEN-P
16D6    RUNIC LETTER EHWAZ EH E
16D7    RUNIC LETTER MANNAZ MAN M
16D8    RUNIC LETTER LONG-BRANCH-MADR M
16D9    RUNIC LETTER SHORT-TWIG-MADR M
16DA    RUNIC LETTER LAUKAZ LAGU LOGR L
16DB    RUNIC LETTER DOTTED-L
16DC    RUNIC LETTER INGWAZ
16DD    RUNIC LETTER ING
16DE    RUNIC LETTER DAGAZ DAEG D
16DF    RUNIC LETTER OTHALAN ETHEL O
16E0    RUNIC LETTER EAR
16E1    RUNIC LETTER IOR
16E2    RUNIC LETTER CWEORTH
16E3    RUNIC LETTER CALC
16E4    RUNIC LETTER CEALC
16E5    RUNIC LETTER STAN
16E6    RUNIC LETTER LONG-BRANCH-YR
16E7    RUNIC LETTER SHORT-TWIG-YR
16E8    RUNIC LETTER ICELANDIC-YR
16E9    RUNIC LETTER Q
16EA    RUNIC LETTER X
@               Punctuation
16EB    RUNIC SINGLE PUNCTUATION
16EC    RUNIC MULTIPLE PUNCTUATION
16ED    RUNIC CROSS PUNCTUATION
@               Golden number runes
16EE    RUNIC ARLAUG SYMBOL (golden number 17)
        * golden number 17
16EF    RUNIC TVIMADUR SYMBOL (golden number 18)
        * golden number 18
16F0    RUNIC BELGTHOR SYMBOL (golden number 19)
        * golden number 19

Here's a scan from the Rune Staff number 144 in the collections of the National Museum of Finland, where we see from the top (twist your head 90 degrees in counter-clockwise direction) the last three of the nineteen "lunation runes", namely

• BELGTHOR - which looks like the Greek small letter phi (U+03C6).
• TVIMADUR - which typographically seems to be a ligature of MADUR and YR.
• ARLAUG - which is a ligature of ÁR (R, the left hand side, the tenth rune in the staff, not "RAIDO/Ræið" which is the fifth one) and LOGR (L, the right hand side, the fourteenth rune in the staff).