This debate will pretty much never die. Even with the current environment of high speed internet and low pings, there is still enough of a difference which folks can argue around forever. Personally I see it as a matter of degree's anymore. "Technically" UDP is the better technology for games and it avoids a number of the downsides of TCP but the differences at the end of the day are fairly small at this point and getting smaller.
The primary issue which folks bring up most often is that because TCP is lossless it will sometimes block IO when a packet is dropped which can increase the effective latency considerably. Such issues can cause hickups in the gameplay and if they are bad enough make a game unplayable. UDP can avoid these problems because most implementations send a steady stream of packets with updated information and missing one packet doesn't hold up later packets which contain more recent data such that the missed packet can safely be ignored. There are a number of reasons that this is becoming less of an issue, at least for games.
The primary reason that this is becoming 'less' of an issue, though by no means gone, is that the internet in general has changed quite a bit over time. Packet loss is actually not particularly common anymore and actually less likely with TCP due to optimizations to the routers which try there best to prevent dropped packets on TCP specifically. Historically I used to measure between 1 and 5 % packet loss from most ISP's depending on time of day, anymore it is at worst around 2% unless they are having actual issues. Also, many routers have a reliability system where rather than waiting on the client or server to resend a packet the router which dropped the packet will automatically re-request it from the closest link. Often such corrections are sub millisecond and barely notable. Finally, even if all the routers are ancient and there is high loss rate, the normal pings between client and server are considerably lower such that the corrections happen in 10-20 ms versus what we used to deal with around 100+ ms.
Now, as Kylotan says, super fast games can always benefit from going UDP. I might argue just how much but that is still a fairly reasonable fact. But, for the reasons I point out above (and lots of other reasons), it is becoming less of an issue and may not matter for most games moving forward.