The Fit to Improvisation technique is something very useful too.

Cactus Music
Play the part with feeling.
There's really no hope for entering data and expecting it to sound like a real musician played it unless you are very skilled and knowledgeable about exactly what it takes to create great music . Of that I'm glad because it makes all the hard work I put into being a musician worthwhile. The day a machine sounds like me is the day the music truly will die. 
Go ahead and try the Humanizing logarithm, it will only add machine generated mistakes to the perfectly mechanical part. It cannot add feeling or create what only a skilled musical would play. 

This is dead on.
 
As much as I can, I perform the parts on a MIDI keyboard.  For the parts I program with a mouse, I spend hours on each MIDI track analyzing and adjusting every note for velocity, timing, and expression based on the context.  It's not easy, it's not quick, it's not perfect.
 
I spent many hours nitpicking the synthesized sax lines on 3 songs I'm currently working on.  I thought they sounded great.  My producer/mixer disagreed, showed me what I was missing, and now I'm hiring a saxophone player to perform what I was attempting.

Volume CCs, velocity and humanize has been mentioned but don't forget about the pitch wheel, mod wheel (or joystsick) and all of the other CCs that can add realism.
 
I agree the best way is to play the line.  A breath controller or wind controller is necessary to add realism to horns, woodwinds and just about every other instrument IMHO.  But unfortunately there is no easy way to add realism to a MIDI part.  It takes time, knowledge of the instrument you are trying to emulate and MIDI controller knowledge.
 
One last thing you can get a close emulation and fool many people but you will never fool someone who plays that instrument.
 
YMMV

The "humanize" function should be named the "number of drinks" function. It may seem humans introduce random timing and other issues, but when you actually take some measurements, it's pretty shocking. Someone like Steve Gadd can lag or lead the beat consistently by a few milliseconds. John Bonham's kick is right on the beat, but the snare is a little bit delayed to give that "big" vibe. It helps if you never quantize to 100% strength; start with 85% strength.
 
But if you REALLY want to know what's going on, AFAIC there is NOTHING better than this ground-breaking article by Michael Stewart.
 
Read it and learn. 'Nuff said.

Thank you Craig. I can't wait to go home now and slide a little snare here and there.

Good point, I almost never quantize to 100 percent. If I have to quantize at all I like to use 80 percent or maybe 85 tops.

Here's another program that has a feature called swing grid ...works for midi and audio ...
sorry to go here , but can this be done in SONAR ?
https://www.youtube.com/watch?v=ZY3fiDV8hIE
 
Kenny

Interesting article. You can't really blame the "android" effect of drum machines on any one factor like timing. The "human" feel isn't just one factor but a series of factors including sample used, velocity variances, note timing, etc. If a DM uses the exact same sample @ the exact same velocity level @ 100% quantization, you'll get the android effect.
 
Some better VIs provide these variances. Most run of the mill VIs don't, so it's up to the user to make them.
 
Another factor is offsetting each instrument so that your ears aren't hearing every instrument strike at precisely the same time.
 
Most, if not all, analog recordings, especially those on tape, drift throughout the entire mix, usually going from slow to fast. I think this "effect" is probably the most humanizing of all and the hardest to emulate digitally.

In my opinion, in the world of modern music, notes on the grid don't sound unnatural to me or most people.  Notes with rigid velocity do, however.  As noted above, having lower velocities on the off-beats sounds better.  For a bass part, for example, I might use Find/Change to set everything on a 0 tick to one velocity and everything else to another, lower velocity.  After that, however, I would check to see if any off-beat notes needed to be emphasized with full velocity. Bass and drums are easy.  An exposed piano part takes time, since some notes are lead notes and some are supporting.
 
It is very important to know how the instrument is normally played.  My favorite true story is about the guy I saw in a music store playing Louie, Louie block chords on an oboe sample and then walking away saying, "That doesn't sound like an oboe."
 
Also, think about what "natural" means.  If it means mistakes or off-beat notes, I wouldn't do it.  If it means smooth and flowing, go for it.
 
For decades we fought to get bass players and drummers to play in time.  Now we have sequencers and everyone complains because they play in time.  Back to my first point, I think the expression is more critical than the timing.
 
DISCLAIMER: I am known for making music with instruments that sound too pristine, so if you want to sound like The Band or The Rolling Stones, completely ignore anything I say.

I read the article Craig linked and it is really good.  I am stupid, though, in that I get confused when they talk about moving events forward or back.  I understand early and late, but with forward and back, I am not sure which is which.