What, nobody has suggested messing with $/ (the record separator)?

Setting $/ to the |---| line will let you read the records one at a time, without having either to glob the entire file or to buffer the lines.

#!/bin/perl -w
use strict;

$/="|--------------------------------------|\n";
<DATA>;        # skip the first (empty) record before the first |---| 
+line
while( <DATA>)# read an entire record
  { chomp;     # to get rid of the extra \n that would mess up the spl
+it
    my %data= (m/^([^:]*):([^\n]*)$/mg); # get field name (before the 
+:) and text (until the \n) for each line

    # %data now holds the fields and their text, and I prove it:
    while( my( $field, $text)= each %data)
      { print "$field: $text\n"; }
    print "\n";
  }

__DATA__
|--------------------------------------|
Date: today
Request: text here text here text here
Name: Joe Bloggs
Tel: 0123 45677
email: joebloggs@bloggs.com
|--------------------------------------|
Date: Today
Request: text here text here text here
Name: John Smith
Tel: 0123 45677
email: johnsmith@smith.com
|--------------------------------------|
[download]

UpdateOf course the original way to parse the record (%data= split /[:\n]/) breaks if the text includes a : so I replaced it with the regexp.