Pros: Decent sound for $150. Decently tight bass for $150
Cons: very poor midrange. Recessed vocals. Tend to break after a few years.
I owned a pair of these. My uncle also bought them. They sound ok for the price. For people concerned with actual fidelity and resolution, you'd be much better off with entry level 4 or 5 inch powered studio monitors. Presonus' Eris 4.5 is a 4.5" stereo studio monitor setup that sounds much better than the promedia- especially with a good source like a decent USB DAC, or even a high end soundcard like an Essence STX. Of course, these don't have a sub. So if you're a basshead and all your music is at a terrible 320kbps or lower, stick with the promedias. If you listen to FLAC/ALAC/WAV or CD's and you want better sound, look at a 4.5 or 5" stereo studio monitor setup. I don't recommend the (strangely popular) Audioengine A5 as an alternative as that speaker is very poor for the price.
Basically, at any price point, there are better speakers out there than the Promedias for the "broke audiophile". For people without good hearing, or who don't know what good sound is, or who are bassheads, the Promedia will be fine for you. However, if you want truly good sound quality out of your computer in a one-time purchase, consider tripling your budget and getting the KEF X300A which is a stereo setup consisting of two nice bookshelf speakers which each have their own internal DAC and class A/B amplification. Those sound like true entry level HIFI. You won't get that out of any computer speaker.
In the end, as all audiophiles know, computer speakers are crap. Why? Simply because the manufacturers can get away with it. The average user doesn't expect much from their computer in terms of sound quality. Those of us in the know, know that you can hook a $50 000 HIFI up to a computer and get incredible sound if you do it properly. All computer speakers from $20 logitechs all the way up to $500 AudioEngine's are crap. Some are more crap than others, like the Corsair SP2500 which is monumentally terrible... but none are good. The only truly good computer speakers that ever existed were the short-lived Klipsch iFi which used two actual HIFI satellites (RSX3) and a proper entry level HIFI subwoofer for really mind blowing sound. They were about $500 back in 2005-2007. Exceptional. These days though it's all gutter grade.
Save up $700 and get the X300As.