...it'd also be important to define
"remake". For example, to me,
"Twin Snakes" or
"Final Fantasy IV DS" are
"true" remakes - they retain the story of the original while sporting
completely new visuals that look and feel contemporary to the time they were released in as well as introduce new gameplay mechanics - they feel like brand-new games and if you aren't familiar with the original games, you wouldn't know any better.
"Metal Gear Solid HD Colelction" or
"Starfox 64 3D" represent the other kind of remakes, the type I like much, much less. Giving the original game high resolution textures or re-writing the original code but ending up with a game that looks exactly the same as the original is pointless in my opinion. A remake should give me a brand-new onlook on a given game, it should feel fresh and relevant. If a brand-new game
"feels" like a 10+ year old one, something has seriously gone wrong with the development process. If that's the aim of the developer, don't even bother with re-writing the code, just port the original as-is - you'll waste less time implementing minute changes nobody's going to notice.
A good remake should refresh a given title, make it interesting to contemporary audiences so that they too could try out the game that may have gotten a little bit rusty over the years - this approach, in my opinion, is superior to putting salad dressing on a rusty product and selling it at a full price... but hey, each to their own.
Aren't the storylines connected?
Only partially. For example, the whole OILIX issue is never mentioned again in the "Solid" storyline despite being a big deal earlier and so on and so forth. In fact, in "Metal Gear Solid 4" we are told that the world economy somewhat collapsed due to an oil crisis - if Solid Snake succeeded in retrieving the OILIX, this should not be the case, everyone should have as much oil as they want. Some characters cross over to the Solid universe, some are completely forgotten. In general, the two series are sewn together with very, very thick threads.