Python 3 - 645 chars

h=0x67452301,0xEFCDAB89,0x98BADCFE,0x10325476,0xC3D2E1F0
L=lambda v,s:(v<<s|v>>B-s)%2**B
B=32
R=range
m=input().encode()
l=len(m)
m+=b'\x80'+bytes((55-l)%64)+m.fromhex(hex(2**64+l*8)[3:])
for C in [m[i:i+64]for i in R(0,len(m),64)]:
 w=[sum(C[i+j]<<8*(3-j)for j in R(4))for i in R(0,64,4)];a,b,c,d,e=h
 for i in R(16,80):w+=[L(w[i-3]^w[i-8]^w[i-14]^w[i-16],1)]
 for i in R(80):f=[b&c|~b&d,b^c^d,b&c|b&d|c&d,b^c^d][i//20];k=[0x5A827999,0x6ED9EBA1,0x8F1BBCDC,0xCA62C1D6][i//20];t=L(a,5)+f+e+k+w[i];e=d;d=c;c=L(b,30);b=a;a=t%2**32
 g=a,b,c,d,e;h=[(h[i]+g[i])%2**32for i in R(5)]
B=160
print('%x'%(L(h[0],128)|L(h[1],96)|L(h[2],64)|L(h[3],32)|h[4]))

Just a golfed version of the pseudocode.

D (759 chars)

Online executable version: http://dpaste.dzfl.pl/f0c8508f

import std.range,std.algorithm,std.bitmanip,std.stdio:g=writef;
void main(char[][]x){
    auto m=cast(ubyte[])x[1];
    uint a=0x67452301,b=0xEFCDAB89,i,t,f,k;
    uint[5]h=[a,b,~a,~b,0xC3D2E1F0],s;
    uint[80]w;
    auto r=(uint u,uint b)=>u<<b|u>>32-b;
    auto u=(uint i)=>[r(s[0],5)+f+s[4]+k+w[i],s[0],r(s[1],30),s[2],s[3]];
    ubyte[64]p;
    p[0]=128;
    m~=p[0..64-(m.length+8)%64]~nativeToBigEndian(8*m.length);
    foreach(ch;m.chunks(64)){
        16.iota.map!(i=>w[i]=ch[i*4..$][0..4].bigEndianToNative!uint).array;
        iota(16,80).map!(i=>w[i]=r(w[i-3]^w[i-8]^w[i-14]^w[i-16],1)).array;
        s=h;
        80.iota.map!(i=>(i<20?f=s[3]^s[1]&(s[2]^s[3]),k=0x5A827999:i<40?f=s[1]^s[2]^s[3],k=0x6ED9EBA1:i<60?f=s[1]&s[2]|s[3]&(s[1]|s[2]),k=0x8F1BBCDC:(f=s[1]^s[2]^s[3],k=0xCA62C1D6),s[]=u(i)[])).array;
        h[]+=s[];
    }
    g("%(%08x%)",h);
}

C, 546 characters

The program calculates the SHA-1 of the contents of its standard input.

unsigned b[16],k[]={1732584193,0xEFCDAB89,0,271733878,0xC3D2E1F0},i,j,n,p,t,u,v,w,x;
char*d=b;a(c){for(d[p++^3]=c,c=0,t=*k,u=k[1],v=k[2],w=k[3],x=k[4];
c>79?*k+=t,k[1]+=u,k[2]+=v,k[3]+=w,k[4]+=x,p=0:p>63;x=w,w=v,v=u<<30|u/4,u=t,t=i)
i=b[c-3&15]^b[c+8&15]^b[c+2&15]^b[j=c&15],c++>15?b[j]=i*2|i>>31:0,i=u^v^w,
i=(t<<5|t>>27)+x+b[j]+(c<21?(w^u&(v^w))+1518500249:c<41?i+1859775393:
c<61?(u&v|w&(u|v))-1894007588:i-899497514);}
main(){for(k[2]=~*k;i=~getchar();++n)a(~i);for(a(128);p-56;a(0));
for(;p<20?printf("%02x",(d=k)[p^3]&255):p>55;a(n*8L>>504-p*8));}

A couple of notes:

1. This program assumes that int is exactly 32 bits. For platforms where this is not the case, the unsigned declaration at the very beginning should be replaced by the platform's unsigned 32-bit type. (uint32_t would be the obvious choice, if it didn't require #include <stdint.h>.)
2. This program assumes a little-endian platform. For a big-endian platform, simply remove the two occurrences of ^3 in the program, and replace the initialization of k[] with the following block: {19088743,0x89ABCDEF,0,1985229328,0xF0E1D2C3}, for a size of 541 characters.
3. For implementations where char is unsigned by default, one can delete the &255 that appears on the final line to save four more characters.

My python code is a little longer but it is fully working.

data="hello world"
bytes = ""
h0,h1,h2,h3,h4=0x67452301,0xEFCDAB89,0x98BADCFE,0x10325476,0xC3D2E1F0
for n in range(len(data)):bytes+='{0:08b}'.format(ord(data[n]))
bits=bytes+"1"
pBits=bits
while len(pBits)%512!=448:pBits+="0"
pBits+='{0:064b}'.format(len(bits)-1)
def chunks(l,n):return[l[i:i+n]for i in range(0,len(l),n)]
def rol(n,b):return((n<<b)|(n>>(32-b)))&0xffffffff 
for c in chunks(pBits,4512):
    words=chunks(c,32)
    w=[0]*80
    for n in range(0,16):w[n]=int(words[n],2)
    for i in range(16,80):w[i]=rol((w[i-3]^w[i-8]^w[i-14]^w[i-16]),1)
    a,b,c,d,e=h0,h1,h2,h3,h4
    for i in range(0,80):
        if 0<=i<=19:f=(b&c)|((~b)&d);k=0x5A827999
        elif 20<=i<=39:f=b^c^d;k=0x6ED9EBA1
        elif 40<=i<=59:f=(b&c)|(b&d)|(c&d);k=0x8F1BBCDC
        elif 60<=i<=79:f=b^c^d;k=0xCA62C1D6
        temp=rol(a,5)+f+e+k+w[i]&0xffffffff
        e,d,c,b,a=d,c,rol(b,30),a,temp 
    h0+=a
    h1+=b
    h2+=c
    h3+=d
    h4+=e 
print '%08x%08x%08x%08x%08x'%(h0,h1,h2,h3,h4)