With Great Power...
Race, Attributes, and Traits
For practical reasons your Spider-Man build should focus on dexterity, wisdom, and strength. While human is a fine race for this build, elves and drow also work quite nicely. You can never go wrong with humans' bonus feat and skill, but low light vision and skill focus, or dark vision and a race where one could be personally chosen to serve a spider goddess are also quite snazzy. Especially if you want to make a cult of evil Spider-Men (you're welcome, dungeon masters).
When choosing your traits, you should focus on what will be most useful to you. Reactionary (+2 to initiative) or Warrior of Old (elf, same bonus) are good for characters who want to go first. Here's a whole post about why that's a great idea, by the by. Other traits like Crowd Dodger (+2 on acrobatics checks to enter another's square or to avoid attacks of opportunity), Soaring Sprinter (+2 on acrobatics checks to maintain balance or to jump), Alchemical Adept (+2 on checks to create alchemical items, and when you fail by 5 or more but don't roll a natural 1 you don't ruin your raw materials. This one's great for those building their own gear.), or Dangerously Curious (gain a +1 on use magic device checks, and use magic device is always a class skill) are all good choices as well.
Just remember, traits that never come into play are traits you'll regret taking. When in doubt, pick a bonus you'll get a lot of mileage out of.
Given all the high-flying acrobatics, ridiculous jumps, and the blue-and-red tights, Spider-Man's obvious class of choice is monk. Not just any monk will do though; the Flowing Monk (Ultimate Combat 58) is perhaps the best choice for Spider-Man. You lose stunning fist, fast movement, your second level bonus feat, purity of body and diamond body, but what you gain is the ability to redirect and trip opponents who try to attack you, as well as dodge bonuses that can make you look like you have precognition. It's the closest thing to spider sense that isn't just acting in the surprise round.
Here's some more details on class abilities.
Reposition, gained at first level, is going to be your bread and butter. This ability allows a Flowing Monk who is attacked in melee by a creature he threatens to use an immediate action to make either a reposition or trip combat maneuver. If the maneuver is successful the enemy is sickened for 1 round (a Reflex save of 10 + 1/2 monk level + monk's wisdom modifier halves the duration) +1 additional round at 4th level and every 4 levels thereafter. If the opponent was charging or using Power Attack then the monk gains a +2 on the maneuver and a +2 on the DC. For those keeping score it's a lot harder to hit someone when you just got knocked flat on your backside.
Unbalancing Counter, gained at level two, says that creatures struck by a monk's attack of opportunity become flat-footed until the end of their turn, though a Reflex save with the above formula negates the flat-footed condition. Yes attacks of opportunity are fairly rare, be patient, this will come into play later.
These monks also gain Flowing Dodge, granting them a +1 to AC for every adjacent enemy, and Elusive Target which allows the monk to apply his Reflex save against enemy attacks for lessened or no damage for the cost of 2 ki. You don't need armor if they can't hit you in the first place.
Aside from these changes the Flowing Monk gains all the stuff you're used to from a monk. You get your wisdom modifier added to your armor class, you gain ki points, unarmed strike damage, and the ability to use your monk level on combat maneuvers. That last one is actually pretty important, especially if you want to be effective when it comes time to trip or reposition your enemies.