It depends completely on the headphone if that will be enough or not. I personally like to think of it in 3 general categories of headphone types when looking at amps to match for them. Type 1 would be normal dynamic driver headphones that have low impedance's, like all the 32 ohm and below headphones. Type 2 can be dynamic driver headphones that are 80 ohm and above with the average type in the 250-600 ohm range. Type 3 would be anything that requires a good deal of power, so any of the planar dynamic driver headphones or the electrostatic ones.
So in terms of what type needs how much power, type 1 needs the least amount, meaning your soundcard will be fine in terms of getting good volume levels, just have a good enough dac as a source. type 1's usually are what can be powered well out of ipods and phones too.
Type 2 are in my opinion the trickiest to match up well because their impedance can fluctuate through the frequency range, meaning if you have a pair of headphones that are type 2 then you will have to do some good research on finding the right match, generally those type need some kind of an amp, but not always will they need a lot of power, but some might. so in this case, just research for the specific headphone what are a few good matches people recommend.
Type 3 is easier to find an amp for, but depending on which specific headphone (since the selection in this grouping is relatively small compared to the other types) you would use, you just simply look for an amp that can at minimum put out 1 watt into each channel. If it can do that then with the exclusion of the electrostatics and he-6, that power output will be fine for them. If you have an electrostatic then you need an electrostatic amp, I'm not super familiar with them, but from what I've seen so far, there isn't too much variety and they will get the job done at least. Oh and the he-6 is just special lol, it needs at least 6 watts into each channel.
So using my set up as an example, I use LCD 2's with an amp that puts out 2 watts at 16 ohms, and according to the company (burson) when I emailed them asking about power output into 50 ohms (which is what the LCD 2's are rated at), my amp would be doing just slightly over 1 watt for them, overall with the clean power the amp provides it works very well. While my previous main uage pair of headphones, the denon's, were a normal dymanic driver 25 ohm headphone and sound loud out of any device they get plugged into. Amps in that case only slightly improve the sound.
I hope this helps, theres other ways to explain all this, and theres also the science about impedance of headphones etc which I am not very knowledgeable on, I just understand what does what lol. I think using the grouping system I laid out here should make picking amps for headphones a little easier for you and anyone else if you are coming at it with no idea about the subject.
