I'm fairly pragmatic, and with dialog choices after dialog choices, it's fairly tempting to just be fairly neutral towards it all (I guess that makes me...a role-player, oh no!). If I do this in The Old Republic, am I going to be handicapped by not having access to either of the presumed bonuses earned by taking one side or another?
So far the only things that I have seen that is affected by your Light/Dark rating are requirements on certain pieces of armor and weapons.
Some character dialog (ie. from your companion) is also driven/derived from your light/dark choices when questing with the companion.
Aside from that, your alignment should have no major impact on your game play.
Yes, you won't be able to use items whose requirement is something like “Dark I” (or “Light I”). But I think it's only a small handicap. (Items with alignment requirement are quite rare, but you can also buy them in special dark/light shops.)
It's possible that the alignment will affect the story in some way, but I don't think I encountered anything like that yet.
There are certain items that can only be used by players above certain Dark or Light levels. The lowest level items I've seen are various Lightsabers.
In contrast to that, there are certain items that can't be used if you have over a certain light/dark level. The lowest level example of these are the various Lightsaber Color crystals. Blue and Green lightsaber crystals can't be used by anyone with Dark 1 or higher. Red and Yellow lightsaber crystals can't be used by anyone with Light 1 or higher.
So yes, there are certain benefits for remaining neutral. As a reminder, you need to have a difference between your two scores of 1000 to become Light 1 and -1000 to become Dark 1.