Traditional Archer:
The keys to being a traditional archer basically require full BAB (or a substitute) and lots of free feats. A "regular" archer build will try to maximize their number of attacks in a full attack and maximize the advantage of having many attacks. This includes flat hit and damage bonuses, but also feats such as Improved Precise Shot, which reduces concealment percentile miss chance (which is normally unaffected by hit bonuses), and Clustered Shots, which means DR only applies once total, instead of once per attack. Utility and quality-of-life feats that let you shoot in melee range, take AOOs, or bounce shots off walls are either necessities for a given campaign, or filler you pick up very late-game.
Classes that fill the role out of the box are the Fighter, Ranger, and Slayer. All of them have access to bonus archery feats - Ranger and Slayer can get them without needing to meet prerequisites, while Fighter has enough feats to meet all the prerequisites anyways. All the classes have a hit and damage bonus in addition to full BAB.
Certain archetypes also convert classes into viable (or more viable) archers. The Zen Archer and Sohei Monk archetypes allow Monks to flurry with bows, which immediately solves the full BAB and bonus attacks expectations. You are under less pressure to use bonus feats to increase your attacks, since you get bonus feats on top of this. The Ilsurian Archer takes some of the Ranger's versatility and transforms it into pure +hit/damage bonuses. The Luring Cavalier has a lot of flat damage, which makes it powerful if you are able to get off a lot of attacks. Insinuator Antipaladin is similar, in that it has a number of bonus feats and a large flat damage bonus.
Some classes do not fit some of the typical archer expectations, but the base strength of the class or a specific interaction of abilities allows it to be competitive. Most notably, the archer Paladin has no bonus feats, but has a hit chance and a massive flat damage bonus that bypasses DR, which reduces the want for feats like Clustered Shots and the need for damage boosting feats. The Antipaladin is similar, since its mechanics are derived from the Paladin's. Certain Barbarian archetypes boost hit chance bonuses necessary for archery, even though Barbarians get no bonus feats. The inherent strength of the class is enough for it to be somewhat competitive with other archers. Warpriest has basically everything except full BAB - it can treat feats it selects in-class as if it had full BAB and 1/2 Fighter level.
Trick Archer:
Classes that are good at being a traditional archer are often effective at being a trick archer. Traditional archers are all about outputting damage, which is fine and all. Trick archers often focus on attacks of opportunity or combat maneuvers, so they can be battlefield controllers. Naturally, this is a very feat-intensive activity. Damage is important, but not as important as in a traditional archer. Classes without damage bonuses may apply, although hit chance is still vital. Feats like Ace Trip or Overwatch Style are on the radar, since they allow you to debuff people on a successful roll, and target more people off-turn, respectively.
Fighter, Ranger, Slayer, and Monk (Zen Archer or Sohei) are strong in the sense that they have the feats to back up a combat maneuver or attack of opportunity build, take the feats to make it ranged, and remain viable as a damage dealer. Magus (Eldritch Archer) should also be under consideration, since it can cast True Strike in the same turn it attacks. However, this is something any Magus can do, so it is not a testament to how effective archer Magus builds are so much as it is to the Magus class in general.
2/3 Caster Archer:
Certain 2/3 caster classes lend themselves to being strong at archery, although not as strong as a full BAB class. The majority of 2/3 casters have an in-class hit chance buff, which allows them to make up for having 3/4 BAB in terms of accuracy. In addition to that, they also often have self-buffing spells that allow them temporary parity with unbowed full BAB characters. These classes make up for having less archery ability by having utility and flexibility from spells and skill points. Notably, arcane 2/3 caster archers can take the Arcane Strike feat, which gives a scaling damage bonus without any hit penalties.
The most notable 2/3 caster archers are Bards and Inquisitors. Both get strong hit and damage bonuses, in addition to powerful self-buff spells and a strong array of skills. Alchemist and Investigator (with the Ranged Study feat) are decent contenders as well, although they are oriented more towards melee or bomb combat and social skills, respectively. Magus (Eldritch Archer) is a strong archer, since Spellstrike allows you to make additional attacks by casting an offensive cantrip as part of the attack. Warpriests have a strong action economy that lets them cast and fight, and have a large number of bonus feats to back it up. Hunter makes a gesture towards being an effective ranged combatant, but they lack the self-buffs, feats, hit bonus, and extra attacks to be truly effective.
Switch-Hitter:
Some classes mentioned above also make good switch-hitters. The key is being able to balance your ranged and melee hit chances. This style minimizes movement and maximizes full attacks - if you can't step up and chop them with your sword, you can shoot them. If you can't shoot them, you can chop them with your sword. If you can't do either, they're dead or a high-level fullcaster. Classes with large weapon-unconditional hit/damage bonuses are key, since they apply to both ranged and melee attacks. Easy access to archery feats, or the ability to substitute attack/damage stats also makes life easier. Your feat choices will basically be Power Attack, maybe Quick Draw, then everything you can afford on the Traditional Archers list. Certain ease of life improvements like Precise Shot and Point-Blank Master should be dropped, since they help you in close-quarters, when you should be using your melee weapon.
Bolt Ace:
Bolt Ace Gunslinger isn't strictly an archer - it's a crossbowman. But I feel that I have to mention it, since it is a viable competitor. The important thing to note is the difference between crossbows and regular bows. Simple weapon crossbows by default require a significant action (full-round, standard, move, or swift) to reload, which means that they typically can only be fired once a round. However, they also typically have a step larger damage dice and 19-20/x2 critical ranges, which is usually considered better than the longbow's 20/x3. Longbows add STR to damage, while crossbows add nothing. However, the Bolt Ace changes that. While Bolt Ace does not alleviate the reloading problems (the Rapid Reload and Crossbow Mastery feats do that), Bolt Ace changes your critical to 19-20/x3 and adds DEX to damage. In addition, you get the nifty ability to spend a renewable class resource to hit against touch AC, which basically guarantees a hit.
