How did you like the 'older' ones? I ask, because I see a lot of people disliking the newer installment - most of them do love the Raimi ones (which were soso imho).
I collected comics when I was younger and still have my collection even though I don't actively purchase anymore. Thus, I generally enjoy all super hero and comic based movies. Of course they aren't all movie masterpieces, but simply watching comic characters come to the big screen is entertaining to me.
I enjoyed the Raimi Spiderman series and thought the actors overall did a good job with the characters. I thought this new one did capture some different aspects of Peter Parker's personality and the effects were well done.
Typically, I try not to overanalyze comic book based movies. I sort of see it like I see the books themselves. Comic characters are not static, but dynamic. They change or evolve with each new artist and writer. They also change over time as our culture changes. Each movie director is going to have a slightly different take on the characters and want to emphasize different parts of the story. Thus, while there might be some specific things that I don't like or appreciate, it doesn't affect my ability to enjoy the overall storytelling experience.
I think this is an interesting change in movies that we really haven't seen that much of where as it is common in the comic world. Those familiar with comic books refer to the Frank Miller Batman or the McFarlane Spiderman in contrast to other artists/writers version of the character. We are beginning to see this on the big screen as well with different directors taking on the same beloved superheros each with their own style. We can now contrast the Burton Batman/Joker with the Nolen Batman/Joker or the Raimi Spiderman with the Webb Spiderman. All in all I think this dynamic is only going to serve as a boon to the fans who will get to enjoy each new iteration of their favorite superhero story.
Growing up my friends and I had the superhero TV shows and cartoons of the 60's & 70's to watch, but we often talked about how cool it would be to see a superhero done well on the big screen. That childhood dream has now become a reality as the advancements made in technology and special effects can now realistically bring the make believe world of superheros to life. From this perspective I say, keep them coming. There's nothing wrong with enjoying a good story.
Edit:
I probably should add that I'm a father to two boys ages 7 and 3. In addition to the big screen there is a whole new generation of superhero cartoons that are really cool as well like Young Justice, The Avengers: Earth's Mightiest Heros, Superhero Squad, and Ultimate Spiderman.