Befunge

Here's a simple one that is arguably a cheat, since it works by reading the program code:

g,1+:72*`#@_:0

And another one that works in a different way.  Note the space at the beginning.  It displays correctly in Befunge-93 and -97, but is slightly off in -96:

 < Just a bit of text to fill the space used to line things up @,*+982_,#! #:< "

Since Befunge has no built-in distinction between code and data, it is hard to say for sure what is a cheat and what isn't.  However, it is possible to write a Befunge quine that works by using separate code and data, much in the manner of a true quine written in another language.  I tried to do it using only two lines, but didn't get far.  But here's what I've got:

4:01p>g,1+::55v         >
 >#v_^#\g10`* <
0^ >1:9+,+:7`#v_0\0\:01p
    p220_@#g22<      >$_^#
4:01p>g,1+::55v         >
 >#v_^#\g10`* <
0^ >1:9+,+:7`#v_0\0\:01p
    p220_@#g22<      >$_^#

The first four lines are the code that is executed; the program reads the last four lines and prints them out.

A while after I did that one, I finally realised the trick! You need to orient it vertically:

vv
11
\\
gg
::
,,
,,
55
55
++
,,
11
++
::
77
33
**
``
##
@@
||
::