Mostly all seasoning packets contain a lot of salt or other sodium compounds, plus pepper, then many add onion and/or garlic powder.
Then they may add whatever flavor it is that makes that product different from its sisters and brothers ("chicken or beef, Italian, tropical, cajun, Spanish, tomato" or whatever).
I often just check out the ingredient list for the packets if I like the basic flavor, then use my own version of those ingredients (dried or fresh) while cooking.
I try to duplicate the ingredients of the various premade "spice mixes" sold in bottles on the spice aisle too, or that I see online.
There are loads of ways to flavor your own rice though whether with dried ingredients or fresh (or a combo)...try some of these:
http://www.google.com/search?q=recipes+flavored+rice
http://www.google.com/search?q=how+to+make+spice+mixes
http://www.google.com/search?q=recipes+healthy+rice
Or just check out the basic kinds of herbs/spices that are often used in one or another culture, and put those things together yourself too.
One simple seasoning for rice btw (I usually make brown rice) is just a little bit of turmeric. Turns the rice bright yellow, is extremely healthy, and smells like popcorn while cooking (also doesn't taste like saffron, the other "yellow" seasoning, which I'm not personally crazy about).
Or I sometimes use a whole "curry powder" (which usually contains turmeric among other spices).
You might also want to try "basmati" (white or brown) rice and "jasmine" rice to get some flavor built right into the rice without adding anything.
As for pasta sauces, those usually have dried powdered cheeses and tomatoes too, and maybe some chicken or beef powder flavorings, as well as the basic salt/pepper/onion/garlic above (and maybe thyme).
Some of those will also have thickeners in them too, esp. the pasta ones, so you'd have to thicken in other ways perhaps.
HTH, and congratulations on avoiding all the excess sodium in those flavor packets too!