The sidekick is another major character that needs to explored. As an extension of the hero, the sidekick acts as an interesting character, especially if handled correctly.
There are three basic types of sidekicks. There apprentice heroes, who are trying to learn how to be a hero from a hero (Robin is obviously the stereotype here). Then there is the “accidental” sidekick; this sidekick always seem to be able to be in a position to help the hero, even though he definitely shouldn't be there (Penny and Brain, for example). Lastly, there is the character that could be a hero in his or her own right, but is somehow tied to the hero (Supergirl (aka Matrix, and the one that's an earthbound angel), when she was employed by Lex, for example).
Each type fulfills a different need, and by exploring that need you can determine which sidekick you should strive towards. The obvious quicky note: You don't need a sidekick. They fill very specific literary needs, and so they aren't right for everyone. Also, don't make the mistake of assuming that everyone likes the idea of a sidekick; when sidekicks were introduced as a sort of avatar for the boys that read comics, the concept was despised (everyone wants to be Batman, no one wants to be Robin). Bear that in mind when you debate one.
The apprentice is the sidekick of choice, especially among male heroes. The apprentice provides a continuation of sorts, and represents the hero's legacy. He is responsible for training the sidekick, and the sidekick becomes an extension of the hero. This doesn't mean that the sidekick can't evolve; rather, that when the hero evolves, the sidekick will be the physical manifestation of that. For example, when Batman was finally able to let go of his past, Dick Grayson was allowed to become Nightwing and become a hero in his own right. Of course, it was quickly realized that Batman needed Robin (without Robin, he became depressed and focused too much on his work; he needed Robin to keep him balanced), and so a new one was quickly found (of course, Jason Todd didn't work out, so Timothy Drake was brought in).
The apprentice is best used when the hero needs to have some sort of symbolic reminder of what he is fighting for, and has some deep issues when it comes to legacy or family. The sidekick is the physical manifestation of the hero's dreams of the future, and provides a link to the past. In short, this particular sidekick is best used as a symbol, but with a conflicting personality to its hero, and abilities based off the heroes (to further enhance the symbolism).
The annoyance is straight comedy relief. The hero keeps getting himself into weird situations, and neds to either be rescued or has to have some luck fall his way; the annoyance provides that escape or luck as needed. The idea is to demonstrate that the hero isn't the end all/be all, and that he has some definite flaws. Penny and Brain are the examples here; Inspector Gadget is always getting himself into danger, and being extracted or rescued by Brain, even as Penny solves the case and provides back-up for her uncle. In pulp, Tonto is probably a good analogue, as he is there to merely provide an extra set of hands for the Lone Ranger. As noted, only use this sidekick when you need comedy relief; it sucks if used for serious reasons.
The equal is the weird one. This character is the hero's inferior only in rank; in all other ways, she is the character's equal or superior. There's a lot of reasons for this, such as some sort of binding spell, the hero has something she needs, or that the sidekick is being punished; the bottom line is that the sidekick is subservient to the hero. Although it can be used for comedy relief, the best way is to show that the hero is still learning his way around, and that the sidekick is going to show him the way; a shaman or pathfinder if you will.
At any rate, have fun with sidekicks; used correctly, they can add so much to your comic. Used wrong, however, and they tend to kill it. So use them appropriately...