Well MvsC isn't really my game, I prefer X-Men vs. Street Fighter. I can give you some tips for doing combos on THAT game, but I'm not sure how much of it will translate to MvsC, seeing as Capcom tweaked certain characters to try to prevent infinites and cheap juggles. Anyways, here's what I can tell you.
For the sake of simplicity, I'm going to refer to the standard air combo as 'zig-zag,' because that's what most combo FAQs call it. On a standard arcade machine the controls look like this:
LP MP HP
LK MK HK
So the standard LP, LK, MP, MK, HP (or HK as a finisher instead) will be called 'zig-zag,' because that's what it looks like when it's performed. Bear in mind that not every character uses the zig-zag combo; like Bison for example, he uses what I call a 'stronger' combo. This is basically LP, MP, HP (or LK, MK, HK; both will work) as opposed to the zig-zag. Also, some characters have such pathetic air-combos that they aren't even worth doing, and with some characters, certain steps in the zig-zag have to be left out. With Cammy for example, you have to leave out her MK, because it will miss 90% of the time.
Now, I'm sure you know how to start the air combo, but I'm going to lay it out for anyone that doesn't already know. Every character has a 'launcher.' This move knocks the opponent in the air, and from that point, if you immediately jump after them, you can do the zig-zag or stronger combo that I just described, if you time it right. Timing is different for every character. Spiderman's zig-zag combo has to be done immediately, or you'll whiff. Other characters, such as Wolverine, are easier to pull off. His moves seem to 'stick,' giving you plenty of time to pull off the next one.
Of course, just standing there waiting for your opponent to walk into your uppercut is a good way to lose a match. So naturally you want to take them by surprise. There are two ways to do this. You can dash in (tap towards twice), hit them with a light punch or kick (depending on the character, punch or kick is more effective; also, with some characters, such as Ryu/Ken/Akuma, you're better off crouching when you do it), and then immediately follow up with your launcher, then doing your zig-zag or stronger combo.
Dash-in combos are probably the most common, however, in my humble opinion, they are also the most predictable. If you resort heavily on this, your opponent will more than likely catch on to what you're doing rather quickly and then counter your dash with a special move of some kind. The alternative to catch your opponent off guard is jump-in combos. This is basically jumping in and attacking your opponent with HP/HK and then doing your launcher and air-combo. Some characters are better at doing this than others. Ryu/Ken/Akuma for example, you have to plant your HK deep into your opponent in order to be able to launch them afterwards, otherwise you'll whiff. Wolverine's jump-in is extremely easy to pull off.
In general, it's best to implement both strategies to start air-combos, but I find that jump-ins are more effective.
Anyways, on to some nifty combos...
Ken
HK hurricane kick, HP dragon punch (enter the dragon punch movements as you are landing)
Dash-in crouching LK, crouching HP, shinryuken (the dash-in can be replaced with a jump-in HK in this or any other combo)
Have opponent in corner. H. hurricane kick, crouching LK (off the ground), crouching HP, Shinryuken
Dash-in crouching LK, crouching HP, *jump* zig-zag (standard air-combo)
Dash-in crouching LK, crouching HP, *jump* LP, LK, up+MK, HP Air-throw (make sure you hold up when you hit MK; when you go to do the air throw, you basically hold towards your opponent for a split second, then hit HP while still holding towards; timing is crucial)
If you have your opponent near the corner on that last combo, you can pull off a Shinryuken before they land. When they are coming down from the Shinryuken, you should also be able to jump up and get in some cheap juggles.
Have opponent near corner. Dash-in crouching LK, crouching HP, *jump* LP, LK, Up+MK, HP Air-Throw, standing LP, LK, crouching HP, *jump* LP, LK, MP, Up+MK, Up+HK, Up+HK (as you are coming down; timing is crucial), *jump*, LP, Up+MK, Up+HK, standing LP, HK Grab (knee-bash).
This combo is insanely difficult, but if you can pull it off, it takes around 70% damage.
Infinite Combo: Have opponent near corner. Dash-in crouching LK, crouching HP, *jump* LP, LK, Up+MK, Up+HK, UP+HK (as you are coming down), *jump* LP, Up+MK, UP+HK, *jump* LP, Up+MK, Up+HK....repeat
Ryu
HP throw, crouching LK, towards+MK, HP throw
The second throw more than likely won't register as part of the combo, but the only way out of it is to tech hit. Easy to do, and excellent damage. This combo doesn't work on MvsC.
Crouching HK, super hurricane kick
The sweep must connect deep in order for the super hurricane kick to work.
Dash-in crouching LK, crouching HP, *jump*, LP, LK, Up+MK, HP Air-Throw, Shinkuu Hadouken
This one is fairly easy to pull off, and is pleasing to the crowd
Have opponent near corner. Dash-in crouching LK, crouching HP, *jump*, LP, LK, Up+MK, HP Air-Throw, *jump* (I know this sounds ridiculous, but after the air-throw, you can in fact jump a second time after your opponent) LP, LK, HK
Wolverine
Dash-in LP, crouching MP, HK, *jump* zig-zag
You can end the zig-zag with a drill claw if you want
Crouching HP, berserker barrage
Nothing special here, just a nifty way to throw berserker barrage into a combo. Berserker barrage can be replaced with berserker barrage X.
Jump-in HP, HK (immediately after the HP, while you're still in the air), crouching MP, HK, *jump* zig-zag
An anti-air combo for Wolverine: As your opponent is jumping towards you, jump towards him and zig-zag, end it with a drill-claw for 5 hits
Wolverine's combos are cool, because the MP that you do right before his launcher actually brings your opponent in closer to you, making his combo even easier to do, and decreasing the chance that you'll whiff.