Non-player characters in the party can make a GM's life simultaneously more and less difficult. Pros include a stronger party, potentially filling a niche the party left behind and a possible quest inlet. Cons such as extra work during combat and another character to flesh out can damper gametime. Some selections need to be made if any of your characters are going to take on cohorts, many of which could save you trouble. Who picks the character to be hired is one, as well as their stats, if they'll share in the treasure, their personality, who will role-play them and if they come prepackaged with quests. Finally you'll need to decide who will control the character in combat. As you can see, some or all of this can be delegated. Is it worth it?
Player characters can either hand-pick their cohorts from a list, seek them out in-game or simply find them as they go. No matter how they come to meet them, it's on the both of you to decide what role is filling the party. When you give them a healer but they wanted a thief, it might not be as fun as if you had collaborated and made a healer-thief. On the other hand player characters who seek out cohorts are technically limited by what's available. It all rests on how much immersion versus how much customization you all want.
Another person in the party means another mouth to feed. Not only that, but what if they want their own share of the booty? I've had one game where the player decided what her cohorts got and how much treasure was going around. Only one game, because the immersion was ruined for me when all she was willing to part with ever was what she wasn't using. In a world where NPCs have motivations and personalities all their own, some of them might be greedy while some of them might be generous. How will the treasure in their share be handled?
On personalities, who gets to decide what type of person the new party member is? In the DM's hands, the person may be quiet to blend in with the rest of the background, or they might be boisterous and raring for adventure. This is normally something that I leave up to the person who will actually be role-playing them. Whoever will be role-playing the character determines many things relevant to that character. First off, if the player does then they've got not only another character to role-play but any role-playing between their main character and the cohort will tend to be mechanical at best. I know of very few players who can actually role-play two different characters at once, all of whom are DMs. The worst choice here is to simply decide the character doesn't have personality or role-play-ability.
A great headache comes from handling far too many pieces on the combat map. Normally I just let whoever employed the cohort control them tactically, since they have some vested interest in them. An alternative to this is for the DM to handle them and let the employing character give them orders in-character. I've heard of games where guest players come in and control the hired help and feel that would be ideal. Remember that these are NPCs and you can veto obviously suicidal or counter to the character's goals. Generally though, I've found that most parties aren't jerks when it comes to expendable characters.
My final note on cohorts concerns whether they have a quest attached to them or not. Did the characters meet them while they were hunting for wyverns? Maybe they'll leave if the PCs don't kill so many wyverns in such an amount of time. Perhaps they are holy warriors searching for an ancient relic. If the players goals depart significantly from theirs then they might not travel with them anymore. The easiest goal to work with is employment: Mercenaries tend to stay as long as the wealth exceeds the perceived risk. An overused goal is the "life debt" or "oath of service:" NPCs should only vow to serve PCs in very rare and special circumstances. Anything aside from that should be considered hired help or common interest companions only. Happy hiring!