Print all but the first three columns

Too cumbersome:

awk '{print " "$4" "$5" "$6" "$7" "$8" "$9" "$10" "$11" "$12" "$13}' things

awk '{for(i=1;i<4;i++) $i="";print}' file

use cut

$ cut -f4-13 file

or if you insist on awk and $13 is the last field

$ awk '{$1=$2=$3="";print}' file

else

$ awk '{for(i=4;i<=13;i++)printf "%s ",$i;printf "\n"}' file

A solution that does not add extra leading or trailing whitespace:

awk '{ for(i=4; i<NF; i++) printf "%s",$i OFS; if(NF) printf "%s",$NF; printf ORS}'

### Example ###
$ echo '1 2 3 4 5 6 7' |
  awk '{for(i=4;i<NF;i++)printf"%s",$i OFS;if(NF)printf"%s",$NF;printf ORS}' |
  tr ' ' '-'
4-5-6-7

Sudo_O proposes an elegant improvement using the ternary operator NF?ORS:OFS

$ echo '1 2 3 4 5 6 7' |
  awk '{ for(i=4; i<=NF; i++) printf "%s",$i (i==NF?ORS:OFS) }' |
  tr ' ' '-'
4-5-6-7

EdMorton gives a solution preserving original whitespaces between fields:

$ echo '1   2 3 4   5    6 7' |
  awk '{ sub(/([^ ]+ +){3}/,"") }1' |
  tr ' ' '-'
4---5----6-7

BinaryZebra also provides two awesome solutions:
^{(these solutions even preserve trailing spaces from original string)}

$ echo -e ' 1   2\t \t3     4   5   6 7 \t 8\t ' |
  awk -v n=3 '{ for ( i=1; i<=n; i++) { sub("^["FS"]*[^"FS"]+["FS"]+","",$0);} } 1 ' |
  sed 's/ /./g;s/\t/->/g;s/^/"/;s/$/"/'
"4...5...6.7.->.8->."

$ echo -e ' 1   2\t \t3     4   5   6 7 \t 8\t ' |
  awk -v n=3 '{ print gensub("["FS"]*([^"FS"]+["FS"]+){"n"}","",1); }' |
  sed 's/ /./g;s/\t/->/g;s/^/"/;s/$/"/'
"4...5...6.7.->.8->."

The solution given by larsr in the comments is almost correct:

$ echo '1 2 3 4 5 6 7' | 
  awk '{for (i=3;i<=NF;i++) $(i-2)=$i; NF=NF-2; print $0}' | tr  ' ' '-'
3-4-5-6-7

This is the fixed and parametrized version of larsr solution:

$ echo '1 2 3 4 5 6 7' | 
  awk '{for(i=n;i<=NF;i++)$(i-(n-1))=$i;NF=NF-(n-1);print $0}' n=4 | tr ' ' '-'
4-5-6-7

All other answers before Sep-2013 are nice but add extra spaces:

• Example of answer adding extra leading spaces:

  $ echo '1 2 3 4 5 6 7' | 
    awk '{$1=$2=$3=""}1' | 
    tr  ' ' '-'
  ---4-5-6-7
  

• Example of answer adding extra trailing space

  $ echo '1 2 3 4 5 6 7' | 
    awk '{for(i=4;i<=13;i++)printf "%s ",$i;printf "\n"}' | 
    tr ' ' '-'
  4-5-6-7-------