Depends on the type. Parrot Pitcher Plants and Purple Pitcher Plants will grow low to the ground.

duno if this helps..this is how mine looks..i rescued it from a death cube..i think its a seracenia purpurea or purple pitcher
{{gwi:552637}}

they do not look great because they were in a death cube and just finished going from green to purple and stuff..but they are catching alot of bugs :)..notice bottom right..slightly to hte left of the pitcher there is a red spec..that is a new growth..so at least i know its not dead

Purple pitcher plants. That's how they grow. DON'T WORRY! Put them in full Sun and keep water in the tray under the pot.

Those don't seem too bad for death cube plants. Raise the water level during the really hot months.

Well it's not a purple pitcher, much more slender-and GREEN!

Excuse the bad picture, the flash ones were even worse(if you can believe that...)
I will attempt a daylight picture tomorrow. Any idea why it lays so vertical?
thnx

Here is a link that might be useful: {{gwi:552636}}

Opps! I meant "why is it so horizontal"

Those are scarlett belle, a mass produced hybrid. They will produce red and white pitchers in full sun. They also become thicker and longer.