I'm going to keep this to names only in the interest of minimizing spoilers.

#Key #: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member
$: Does not count towards 'Paramour' achievement

All listed relationships except for Diana Allers count for Paramour.

#Male Shepard

Ashley
Liara
Tali #
Miranda #%
Steve Cortez ^%
Kaidan ^
Jack #%
Diana Allers %$

#Female Shepard

Kaidan
Liara ^
Garrus #
Samantha Traynor ^%
Diana Allers ^%$

I'm going to keep this to names only in the interest of minimizing spoilers.

Key

#: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member
$: Does not count towards 'Paramour' achievement

All listed relationships except for Diana Allers count for Paramour.

Male Shepard

Ashley
Liara
Tali #
Miranda #%
Steve Cortez ^%
Kaidan ^
Jack #%
Diana Allers %$

Female Shepard

Kaidan
Liara ^
Garrus #
Samantha Traynor ^%
Diana Allers ^%$

I'm going to keep this to names only in the interest of minimizing spoilers.

#Key #: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member

All listed relationships count for Paramour.

#Male Shepard

Ashley
Liara
Tali #
Miranda #%
Steve Cortez ^%
Kaidan ^
Jack #%
Diana Allers %

#Female Shepard

Kaidan
Liara ^
Garrus #
Samantha Traynor ^%
Diana Allers ^%

I'm going to keep this to names only in the interest of minimizing spoilers.

#Key #: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member
$: Does not count towards 'Paramour' achievement

All listed relationships except for Diana Allers count for Paramour.

#Male Shepard

Ashley
Liara
Tali #
Miranda #%
Steve Cortez ^%
Kaidan ^
Jack #%
Diana Allers %$

#Female Shepard

Kaidan
Liara ^
Garrus #
Samantha Traynor ^%
Diana Allers ^%$

I'm going to keep this to names only in the interest of minimizing spoilers.

#Key #: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member
 $: Confirmed as Counts for Paramour

#Male Shepard

Ashley $
Liara $
Tali #$
Miranda #%$
Steve Cortez ^%$
Kaidan ^$
Diana Allers %

#Female Shepard

Kaidan $
Liara ^$
Garrus #$
Samantha Traynor ^%$
Diana Allers ^%

I'm going to keep this to names only in the interest of minimizing spoilers.

#Key #: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member 

All listed relationships count for Paramour.

#Male Shepard

Ashley
Liara
Tali #
Miranda #%
Steve Cortez ^%
Kaidan ^
Jack #%
Diana Allers %

#Female Shepard

Kaidan
Liara ^
Garrus #
Samantha Traynor ^%
Diana Allers ^%