I ain't a guitar player and it is easier to DI those dang things.  But I prefer to mic them.
 
Bass is good to DI and is much easier to do that when both it and guitar are playing.
 
Synths?  I'm still experimenting.  I jsut bought a little 8 inch combo to mic soft synths w/.  Worth a try.
 
@
 
 

I ain't a guitar player and it is easier to DI those dang things.  But I prefer to mic them.
 
Bass is good to DI and is much easier to do that when both it and guitar are playing.
 
Synths?  I'm still experimenting.  I jsut bought a little 8 inch combo to mic soft synths w/.  Worth a try.
 
@
 
 

Bass is always DI'd in my studio/recordings. Just way simpler.

maximumpower
Stupid question... whether you mic or not, don't you have to go through your interface to get it into your DAW?

Not a stupid question, and yes, you do go through your interface.
A common chain would be Guitar > Amp > Mic > Pre-amp ? Interface.
You might not need the pre-amp if the pre's in your interface are of reasonable quality
 

Second stupid question... When using a mic, are you actually recording what you hear or what the microphone hears?

Another non-stupid question. Yep, you're recording what the microphone hears, so it always pays to enable input echo, put on headphones and experiment with moving the mic into different positions in front of your cab.
Half an inch difference in any direction can make a HUGE difference to your recorded tone.
Don't forget to try different speakers as they can all sound different to one another.
Also try putting a second mic up a few feet away and get a bit of room tone.

I suppose the question was aimed mostly for guitars, but all apply! Because I realize I'll most likely have to do it all eventually anyway. Thanks for responses so far!

Similar to MakeShift and IK Obi, I've done both. I prefer DI most of the time because it is simpler. I use Guitar Rig 4 and I like the tones I get. I've used AmpliTube but it was the version that came with (I think) Guitar Tracks. I haven't tried the newer version of it yet but I have a friend who has and he likes it.
 
I second the lack of dynamics/responsiveness but I don't play with a lot of dynamic changes in the same part. I may have different tracks with different patches that are played differently, but, for example, most of my leads are more legatto melodic types (at least that's how I think of them) and don't need dynamics.
 
The main thing I'll go to micing an amp for is when I want feedback. I can't get that through my monitors.
 
I still struggle finding the best mic placement when micing. As a one man shop it's hard to adjust mic placement while trying to play at the same time and trying to hear through headphones when I want enough volume to get feedback. And, when I use amps I use 2 at the same time, micing one speaker of each (plus I have a DI feed after my pedal board but before the amps).