Character Analysis
In simplest terms, Alfred Pennyworth is the reason Bruce never shows at the hospital with weird cuts and bruises.
He's Bruce's butler, manservant, and stalwart Man Friday: there to cover the legwork required to get him all that snazzy gear, and to stitch up those dog bites with competence and panache (a past as a combat medic will do that for you). If Bruce needs it, Alfred's got it, handy when you're taking on the kind of problems he does.
But Alfred is more than just a guy to press the cape and change the linens. He acts as a father figure to Bruce, and frankly to Rachel too: giving them advice and being there to support them when they need someone to lean on. He can give them a good talking to if they need it, and he's always ready with a sharp quip to remind them that they're not invincible.
BRUCE: Targeting me won't get their money back. I knew the mob wouldn't go down without a fight, but this is different. They crossed the line.
ALFRED: You crossed the line first, sir. You squeezed them, you hammered them to the point of desperation. And in their desperation they turned to a man they didn't fully understand.
BRUCE: Criminals aren't complicated, Alfred. We just need to figure out what he's after.
ALFRED: With respect, Master Wayne, perhaps this is a man that you don't fully understand either.
In the end, he loves them as much as any parent could and fills up that void left by the Waynes' death as well as any man ever could. This doesn't differ much from most other depictions of Alfred out there (though The Dark Knight makes him a cockney working man rather than a snooty aristocrat, to better fit actor Michael Caine's persona). Neither does the way his caring for his charges leaves him making decisions that he shouldn't.
This happens most notably when Rachel gives him a letter to give to Bruce, one that tells Bruce she's going off with Harvey and will never be with him romantically. (Not unreasonable, considering his nighttime hobbies.) Alfred chooses to burn the note after Rachel dies, in order to spare Bruce the pain. We certainly know why he does it: as the resident father figure, he wants to spare his "son" any more agony. Rachel is gone, he reasons, and her motives don't matter anymore. Better to keep that from Bruce than pour salt in an already throbbing wound.
As we said, it's a noble sentiment, at least in theory. In practice, though, it turns out to be a big, bad mistake (though we don't know how big until The Dark Knight Rises four years later). In the first place, it instills a false belief in Bruce that Rachel would have been with him, something that keeps him from healing and moving on. More importantly, it denies Rachel the weight of her choice. She's going to be with Harvey, that's the end of it, and she needs him to understand and respect her choice. By burning up the letter, Alfred takes that away from her—the last decision she ever made—and tarnishes her memory in the process.
But this, too, is a lot like a parent. Parents mean well, but they mess up sometimes and in their effort to keep their children safe, they usually make them even more vulnerable. Poor old Alfred falls into that trap, right when Batman himself is making a similar mistake. For all the good things he does for Batman, he lets him down in the way that matters most. Bruce and Alfred are closer together than they thought: making the same mistakes at the same time for the same reason. It tinges their steadfast relationship with something a little more tragic, and if you tune into The Dark Knight Rises, you can see the ways that failure comes back to haunt them both.