Your "internet connection" may not be what you think it is. You can't assume that just because you can connect to one service just fine that means you should be able to connect to any other service just fine as well. Your connection to the nearest head-end for your ISP may be fine... but that doesn't mean the path to every one of the thousands upon thousands of networks that make up the internet is also fine. You may take 5 hops just to get out of your state and onto a third party's trunk line that carries you to Montreal by way of another 6 or 7 hops, before you get pushed onto Ormuco (SE's ISP in Canada), where you get switched some more before finally hitting SE's network. There are MANY potential points of failure along the way. For a sort of visual, here is a route to one of the lobby servers for FFXIV:

Code:
 0  G75VXLAP [10.10.100.10]
 1  LPTSRV [10.10.100.1]
 2  cpe-75-176-160-1.sc.res.rr.com [75.176.160.1]
 3  cpe-024-031-198-009.sc.res.rr.com [24.31.198.9]
 4  24.31.196.212
 5  be33.chrcnctr01r.southeast.rr.com [24.93.64.182]
 6  bu-ether44.atlngamq46w-bcr00.tbone.rr.com [107.14.19.46]
 7  0.ae0.pr0.atl20.tbone.rr.com [66.109.6.171]
 8  twc-telus.pr0.chi10.tbone.rr.com [66.109.9.70]
 9  ae-11-11.car2.Montreal2.Level3.net [4.69.141.1]
10  ae-11-11.car2.Montreal2.Level3.net [4.69.141.1]
11  ORMUCO-COMM.car2.Montreal2.Level3.net [4.59.178.74]
12  192.34.76.10
13  199.91.189.242
14  199.91.189.74
There are at least 10 unique networks involved in getting from point A to point B, and some of them switch through extra devices along the way as well.

SE recently announced that Ormuco was having issues along certain paths the other night (check the notices in the launcher or the Lodestone). Less than a week ago, Charter also admitted they were having severe routing issues for players in some regions.

This kind of thing happens all the time, and when it does happen the path to the server needs to be traced to isolate the problematic segment and either get that hop addressed, or alter routing to avoid the troubled segment(s). To that end, our ISP's enter into peering/transit agreements with multiple ISP's to help us get from our ISP's networks to someone else's network. Otherwise, we would only be able to connect to people that subscribed to the same ISP, and even that may be limited regionally as they may not have dedicated trunks that run cross country, much less transcontinental connections.

More often than not, we find the problems are more within the sphere of our ISP's influence than SE's. You can prove this by using a VPN. If things improve dramatically, there is a problem along the route your ISP has assigned you to use...nothing to do with SE's servers in such a scenario. But to get such issues addressed, you will need to be dealing with higher tiers of support than the guys that answer the phone and look at your modem, or the the guys that come check your lines. You need to deal specifically with Tier3, which will require escalation...possibly even demanding that you speak to some supervisors if they give you the run around. Alternatively, you can try their support portal or twitter/facebook--those contact methods tend to get you to higher tiered support with less hassle.