Always, always try to recover from up high. Against good opponents, and you can never be too sure so just do it, they will grab you if you cypher up from below since cypher has no sweet spot. By grabbing you in midair, you lose your cypher completely as long as they don't grab attack. When you shake out of it, you don't have an up+b anymore and you fall to your death. So, at all costs, try to recover from up high be it via bomb jumping or pulling out a nade etc.
IF this does happen, hold down and spam the B button like mad. Hopefully as soon as you break out you can manage a C4 bomb jump and try to recover again. It's worked for me a couple of times.
Common opponents:
Metaknight. Smart grenade countering usually takes care of him. Stops the mach tornado in it's tracks. Make sure your air dodges are well timed to avoid incoming shuttle loops. He's quick but the nades will throw off his flow. Watch out for his rapid slash to dsmash, if he's rapid slashing, DI backwards.
Game and Watch. This guy is a pain the ***. The bair especially. So far, the only counter I have for it is power shield then hold the shield until the 2nd to last hit (there's a delay between the second to last hit and the last hit) and immediately up tilt. But this is assuming the G&W did not DI backwards out of safety. Make sure to always attempt to tech the down throw so you don't get dsmashed. He'll use uair often to keep you airborne where you're most vulnerable. Sometimes using dair and fast falling helps. He's light though, tilts will do the trick, as well as mortar slide, and grenade countering works to an extent if he get's greedy with his aerials and forgets to space them. Still you're in for a tough match.
Pikachu. AKA mouse spawn from hell. I seriously don't know how to deal with him. This matchup is pure ****, but you just have to be very cautious. Don't get fooled by Quick Attack Cancelling, just roll out of the way. He'll often try fair to dsmash. A nice trick against this is holding your shield after the fair, let the dsmash go off for about half a second, then dodge. You'll usually avoid all the hits this way and can be ready to counter. Watch out, pikas mix it up with grabs or utilt. His thunder edgeguarding is also especially effective against Snake, it'll take some smart delaying/DI/air dodging for your recovery on your part to get past it. But like I said, this matchup will have your Snake crying for mommy lol.
On gimps, there's Falco who'll chain grab you till you're at the edge and do a dair. Make sure you don't panic and just let him dair you and then use your second jump and then cypher. You may have to bomb jump to get higher. Rule of thumb vs Falco, DONT GET GRABBED. Don't do things that would put you in a vulnerable position, like predictable tilt spam or mortar slide spam. Don't do laggy attacks when there's room to punish afterwards. You can (non-contact) mortar slide immediately from prone position, use this to your advantage since you'll be using prone to avoid lasers. Just non contact mortar slide when you see Falco hesitate/approach and you're in range.
Uhh...also...watch out for DK's...they are simply the ultimate Snake gimper in the history of Snake counters. If a DK throws you off using down throw, he's likely going to follow up with a spike using fair or dair and anticipate your second jump so you get hit and lose it. To avoid this, as you're thrown, DI backwards and jump away from his fair/dair and try to up B back. You may have to bomb jump to get a better height too.
I freaking hate DKs now. Dare I say it, more than Olimar.
edit:
-Rapid Jab stops Wario's motorcycle rush.
-Rapid Jab stops a D3's chaingrab (unless he's a very good D3 that delays/mixes up his chaingrabbing)
-Rapid Jab stops missiles from samus, and pikachu's thunderbolts
-Rapid Jab stops an opposing Snake's nikita.
I bet Rapid Jab can stop more things but that's what I can think of lol.
Against the harder matches (aka DK/pika) it wouldn't hurt to use Marth. I'd say you probably have a better chance, but don't quote me on it since I don't use Marth lol. I just know those matchups are terrible for Snake. Also check out the character matchups thread if you'd like, there's good strats in there for other characters:
http://smashboards.com/showthread.php?t=158037
This is coming from me going to a few tourneys recently.