The first screenshot appears to show all notes laid down significantly early - like 1/16 or more. I see only one (3rd from the end) that looks like it's maybe only a few ticks early. Ordinarily, a perfectly timed MIDI event will be recorded late by just 2-5ms (4-10 ticks at 125BPM), depending on the responsiveness of your controller/keyboard and MIDI input transmission time of your interface. Having notes consistently laid down 240 or more ticks early and visibly off the grid at that zoom level points to a problem with the relative timing of the audio clock and the MBT grid.
 
Assuming you have no Timing Offset (ms) entered in preferences to alter the relationship between the audio clock and the MBT grid, this should not happen, but some audio-MIDI interfaces or combinations of separate audio and MIDI interfaces in some systems seem to do this. It's pretty rare, and I don't know that anyone has ever gotten to the bottom of it other than by deliberately setting a Timing Offset to compensate, but this is to be avoided if possible because it gives different results for hardware and software synths, and alters the relationship the wrong way for playback when set to compensate for recording offset.
 
What are you using for audio and MIDI inteface(s), and what driver mode? ASIO is generally preferred, but you might try switching to whichever mode you're not currently using to see if it has any effect.

If all we were looking at is latency it would put the note after the beat. Latency causes a delay. You play the note where you think it belongs, but latency causes a slight delay so it lags behind the beat a bit. Most people can compensate for this so I don't think it's straight forward.
 
When I was a kid I played drums and took lessons. I spent years playing to a metronome and that helps you keep time, but when you're learning it's hard to tell if you're rushing or dragging the beat - that's one thing that an instructor should help you with. If you practice, how much time have you put in with a metronome and instructor? I think that's a nice thing about midi, you don't need an instructor, you can check the prv. Being able to nuance your timing is part of the expressiveness of music.
 
I think there are two questions. The first is does it sound ok? The second is do you want to improve? If you want to improve then practice your timing.
 
I'm an amateur, I'll practice a part until I'm comfortable with it and then I'll record it (and that may require several takes), but I don't check the prv, if it sounds right then it's a take. I do like to improve so I practice and try to get better and over the years that has included working on my timing playing with click tracks and checking the prv.

I agree with brundlefly on this one, unless it is the player. Having said that, anticipating the beat by 1/16th note is a cool sound, it has a sense of urgency, rather than laying back in the pocket. Does the song you're playing have a certain drive to it? If so, playing ahead of the beat is par for the course. Copy the track and quantize it to fall right on the gridlines. Changes the feel of it, yes? sometimes the player is unaware of it. In college, When I took a sight reading jury final, the instructor asked me if I listened to a lot of jazz, because I tended to swing 1/8th note groupings. I actually counted it that way, and had to replay it in "robot mode".

Are you listening thru headphones or monitors? Don't forget 1ms is about 1ft from the sound source and may account for some of the delay.
 
No, wait. You're ahead of the beat, not behind. Never mind...

are you guys getting to technical here ;-) if it sounds right, it is right ... there's no point to move anything a few ticks later because it visually does not align with grid lines (well, you can but it won't feel/sound as before) ...
 
playing a virtual instrument is subject to latency from your interface (which is probably small if set to low buffer but there is always latency) ... and if you play by what you hear, you might actually naturally be compensating for that delay i.e. hitting the keys slightly early so that the sound arrives at your ear when it should i.e. properly aligned with the groove you are playing along...
 
 

tenfoot
 
For some more disturbing news, record some vocals and have a look at it in melodyne:)
 

RehabRob
are you guys getting to technical here ;-) if it sounds right, it is right ... there's no point to move anything a few ticks later because it visually does not align with grid lines (well, you can but it won't feel/sound as before) ...
 
playing a virtual instrument is subject to latency from your interface (which is probably small if set to low buffer but there is always latency) ... and if you play by what you hear, you might actually naturally be compensating for that delay i.e. hitting the keys slightly early so that the sound arrives at your ear when it should i.e. properly aligned with the groove you are playing along...

"A few ticks", no, but 240+ ticks (if I'm interpreting the screenshot correctly) is huge. I agree there is some tendency for the performer to automatically correct for latency or instruments with a slow attack, but this is probably on the order of 30-60 ticks (as is 'feel' or 'swing'), and would not account for the discrepancy the OP is seeing. And in the example he was focusing on hitting keys in sync with the click, so automatic latency compensation would not have been a factor.
 
I'm pretty sure there's an actual technical problem in this case that needs fixing.

All your responses have lot of useful information.

Yes its a technical problem. 

I was able to pin point out the issue with the help of Sonar's Record Synth audio.

Was bit occupied. Didn't got time to post it here.

Will post a detailed message. But for now. Yes it is a technical problem as a result of latency. It seems every one will face this issue. But the latency will be very low so its negligible. But if you are recording using your inbuilt sound card, you gotta take a notice of this. You all can face this issue in every DAW.

Yes, synth Recording is a good way to check for sync. I was going to suggest simultaneous MIDI-Audio recording from a keyboard synth if you have one (which will also reveal actual audio input latency), but internal Synth Recording is a good alternative. If the MIDI is very early relative to the synth audio, you know something is not right, and interface latency (both MIDI and Audio) is out of the picture.
 
Keep us posted.
 
I have suggested this (often to no avail, unfortunately) in the past, but you might want to try setting IgnoreMIDIInTimeStamps=1 in TTSSEQ.INI
 
P.S. Below is one ancient reference to the functionality of this parameter from a Baker; personally I've never found that it had any effect one way or the other with any of several MIDI interfaces, but then I've never had the kind of timing discrepancy you're encountering, either:
 
     http://forum.cakewalk.com/FindPost/1161

I agree with some of you guys telling  'if it sounds right, it is right'. That's true that's the only thing that matters. What I have noticed always is that when I play and record it sounds so perfect but when I play back the recorded midi take I notice a bit of unnatural sync. Very minute though. I move the recorded notes a bit towards the grid and it sounds better.

here is what I did.
I recorded a take with synth audio track armed. 
This is what I got



Zoomed in


The audio was 10ms delayed than the midi note.

Then I noticed that My ASIO reported total roundtrip latency is 10.9ms as well




I changed my ASIO buffer size to max.



Now the reported total roundtrip latency is 100.9ms

Now I recorded a take again with synth audio track armed.

Got this



Zoomed In



The audio here was 100ms delayed than the midi note 

So although the midi note got recorded few ms ahead of the beat the audio is where it should be. 
So I can leave the notes there itself right? NO NO NO!!!! BIG NO!

Now I deleted the recorded synth's audio. And recorded it again(only the audio from the pre recorded midi). This will help me know whether the audio will still be delayed than the midi note while playing back the recorded midi.

This is what I got 
For 10ms



For 100ms



As you guys can see. The audio gets played just where the midi notes are without any delay.

What can we conclude from this-

1.While recording if there is latency in roundtrip. There is a latency between audio and midi. We humans will play the notes slightly ahead so that our ears will perceive the audio in sync with the timing of the metronome/other instruments. Yes the audio we hear while we play is  correctly in sync, but inorder to sync the audio we compromise by playing the notes slightly ahead
OR
The DAW records them slightly ahead so that we hear the audio in sync. (I am not sure which case is true but either way we know that the midi is recorded slightly ahead depending on the latency)

2.However while we playback there is no latency between audio and midi and we end up hearing the audio aswell slightly ahead of the beat(if the midi notes are ahead of the beats)

 How can we fix this

1.Move all the midi notes exactly __ms forward(depending on your reported latency)
2.You can also record the audio along with the midi while recording and then keep the audio and delete the midi.(This is not a good idea though as you cant edit the midi notes.  what's the advantage of using midi then)
3.Record the audio along with the midi and then move and align the midi notes straight to the audio transients and go on and delete the audio.

Point 1. will work for me.

But is there someother way to do this much more easily?

brundlefly mentions of having timing offset in preferences. Can that help. May be!

Or may be Bakers can provide us with an potion to override this automatically in sonar. May be we need a Midi Delay Compensation  Guess we will be the first to introduce that. 

I am no expert. Just a lay user wondering of stuffs. If I have noted something technically wrong here please correct me.

Thanks.