So companions are introduced to you in this game fairly early if you follow the main quest a couple quests in. This first companion is Lydia, and her job is to be your housecarl, and she has some dialogue explaining her duties to you, but then becomes relatively boring. She doesn't seem to level up with you or improve in any way that matters. Sure you can deck her out in nice gear, but it doesn't stop the fact that she become irrelevant later in the game.
Basically she doesn't have any staying power besides the first hours of the game, which is really disappointing. I'm a little upset that Bethesda ignored their improvements going from Oblivion to Fallout 3. And the massive upgrade followers got in New Vegas (Dev'd by Obsidian I know).
Where is character development for any of the companions in Skyrim? Sure some have a radient task for you, and fewer will have a particular quest involving them, but the majority of the time the characters have little to nothing to say, and no growth as a person after travelling with you or delving into their personal lives.
Now, I will adress that Serana, a companion in one of the DLC's is by comparison, deeper and interesting. Changing her attitude throughout the questline involving her, and ultimately through your conversations and actions, she can change things about herself that affect her as a person.
Why can't we have had a few more like her? Trade in the vast quantity of followers Bethesda has provided, for more interesting, deep, and involving characters. Quality> Quantity and it shows.
TL;DR= More better written companions, that will stay relevant even later in the game.