if you wanted 5.1 for that budget...
you might want to check out the z506 which is $60 on amazon right now
http://www.amazon.com/Logitech-Surround-Sound-Speakers-Z506/dp/B003VAK1FA and while it might not be top-of-the-line in terms of sound quality it certainly has much value for the money spent and will satisfy most people.
its hard to find good sound for under $100 and 5.1 so i only listed the above. i would avoid genius speaker sets like the plague as they are only "loud" but are completely lacking in terms of good "sound quality"
if you wanted 2.1 for that budget..
you might want to look at the jbl creature iii
http://www.amazon.com/JBL-Creature-III-Self-Powered-Multimedia/dp/B002TLSTGA/ref=sr_1_1?s=electronics&ie=UTF8&qid=1406515302&sr=1-1&keywords=creature+iii which get good reviews in terms of sound quality
the logitech z623 can be had for that budget and will sound just a bit better than the 5.1 z506 in terms of sound quality
http://www.amazon.com/Logitech-980-000402-Speaker-System-Z623/dp/B003VAHYTG/ref=sr_1_1?s=electronics&ie=UTF8&qid=1406515360&sr=1-1&keywords=logitech+2.1
i would avoid the klipsch promedia 2.1 as the subwoofer is too large and completely overpowers the satelites. otherwise, sound quality is quite good and so is build quality. i bought this and returned it the next day (i ended up spending much more money on a complete klipsch hifi system instead)
if you were open to 2.0 systems...
the creative t40 (or t20, the next step down)
http://www.amazon.com/Creative-GigaWorks-Multimedia-BasXPort-Technology/dp/B001S14DYO/ref=sr_1_1?s=electronics&ie=UTF8&qid=1406515311&sr=1-1&keywords=t40 are well known for good sound quality. however, since they lack a subwoofer they are very bass-light.
for under $100 it is also possible to build a mini hifi system such as this http://www.cnet.com/news/build-your-own-desktop-stereo-for-under-70/ which will sound good for the money. no subwoofer is included but you could add one later if you wanted more bass. they quite easily will beat any $100 speaker set in terms of quality, you might even compare them to sets up to $200.
if you want more hifi suggestions then read this
http://www.head-fi.org/t/678857/looking-for-a-2-0-2-1-set-of-computer-speakers-for-under-100
i'd also like to note that i dont suggest bose speakers. generally all you get is overpriced trashy-built speakers in all but their absolute top-of-the-line speaker models. for the money you can certainly do better. they might sound fairly good but in general i dont consider them worthwhile.
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