There is an unavoidable minimal latency when shooting packets across the whole planet, because the speed of light is an absolute maximum for the transfer of controlled information, according to the Laws of Physics as we know them.
("Controlled" means that I am not talking about so-called quantum teleportation, which works in lab conditions, but does not let you choose the information that you send. Also, even if the laws of physics can be broken in abstracto, it is doubtful that existing routers and, even more so, infected PC, will be so kind as to enact the break for you.)
Thus, the minimal time for a roundtrip between North America (East Coast) and Europe is about 40 ms (20 ms for each direction). In practice, observed roundtrips are close to 120 ms (that's what I personally get, ping time from my home in North America to my server in France), which is bigger but still in the same order of magnitude. Assuming this crude measure to be representative, we may then claim that the latency will be about three times what it would take for light (in a vacuum) to walk the total distance. This leaves us enough juice to do more than two circles around the world (even equatorial circles) and still be at sub-second latencies. One second of latency is not comfortable and you certainly do not want that for any gaming-related activity, but it will be far from timeouting.
This can be compared with Internet access through geostationary satellites: since such a satellite orbits at 36000 km above the Earth, ping time is always bigger than half a second (that's four 36000 km trips for each ping). Such latency can be heard when phoning people in remote places (where there is no transoceanic cable): the extra latency always gives the impression that the guy at the other end is not fully awake. I certainly would not like a satellite-based Internet access for my own usages, but there are people who succeed at it.
As for security, each hop is indeed a good way to cover your tracks, as long as the proxies do not propagate the information. Normal proxies add their own HTTP header line to make it clear from whence the request originally came; an anonymizing proxy will omit that header. When proxies are all over the World, it becomes complex for Law Enforcement Agencies to rewind the whole cascade, because they have to seize each successive proxy and find log entries which point to the next (previous) proxy machine. International police being what it is, competent attackers who do a lot of hops consistently evade legal retaliation (but competence is a rare thing in this World).
Of course, the Hollywood World Map with lights showing the whole path is a pure fantasy; and even if it existed, it would indicate a spectacular failure for the attacker: the whole point of doing many hops is to make it difficult to rebuild the complete sequence of proxies, regardless of whether the rebuilding is for feeding a World Map with blinking lights, or to unleash a police squad on the perpetrator.