What qualities should I look for when hiring call center agents?

I agree that their "phone quality" is key! In addition to their vocal clarity, enunciation (intelligibility to your audience), and I would also suggest that there are two additional traits you should look for in these folks: 1) you should be able to "hear them smiling through the phone"; 2) you should also be able to "hear them listening attentively throughout the call".

Beyond that, if your clientele are multi-lingual, you may want to find some folks equally fluent in those languages, or those that have a great deal of patience with clients that speak English as a 2nd language.

While most everyone can use a telephone - not everyone is cut out to work in a Call Center environment. Someone may have “The Right Stuff” to be a great Customer Service & Support CSR – it doesn’t necessarily follow that the same individual is also cut out for the more demanding & sales-oriented requirements of Up-Sell/Cross-Sell/Customer Win-Back – let alone a more proactive Outbound TeleSales or TeleCollections job.
Typically there are three grades of Agents found in a Call Center: (Above Average), (Average), and (Below Average).
(Above Average) Agents seem to have “The Right Stuff” that pushes them to succeed & a natural compatibility with the duties of the position. They work hard - exceed expectations - do more than asked - achieve high-quality consistent results - can always be counted upon - need little direction & work extremely well with everyone.
(Average) Agents perform their duties adequately enough “to get by” - but no better. They are the partially competent. Generally they’re strong from a Skills standpoint but missing a key ingredient or two from a Job Fit standpoint.
(Below Average) Agents are the people who just don’t fit somehow. Sometimes they’re good people in the wrong jobs. They need extra coaching & supervision just to achieve average results. Often they cause unnecessary conflict. (Below Average) Agents have the Highest Levels of Absenteeism, Lowest Levels of Productivity & Sales, Poorest Performance & Customer Satisfaction Ratings, and generally have a Negative Impact on Team Morale. They represent the real problems in a Call Center workforce. While (Average) & (Below Average) Agents may seem fully qualified at the Interview Stage – they’re a Poor Job Fit – the cost of hiring them is enormous – with little value add to an organization.
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I agree with both Michael and Ralph but I would add that the ability to close the call quickly is another good trait. Time is money and the longer an agent is on the call with one customer the less productive he/she is and depending on the size of the center can significantly decrease response time to other callers.