Nobody makes PC speakers like they used to
Altec Lansing, which used to be one of my favorites, is now near-non-existent. Logitech has reduced the quality of even its top-end line. Klipsch is now a rarity.
What most folks are suggesting - bookshelf or larger / pro / home theater audio - is probably where you might be considering if you're thinking upgrading.
I personally have been looking at "upgrading" from PC speakers (I've owned Altec Lansing ADA305, Altec Lansing MX5021, Logitech Z-680, and Logitech Z-5300e). Specifically, I am looking at creating a "budget" setup, combining the following:
1 center channel with tweeter - haven't picked yet. ~$50-$100
1 pair Sony SS-5000 (R/L) - $150 total on Amazon
1 pair Sony SS-1000 (RR/LR) - $64 total on Amazon
1 woofer - haven't picked yet. ~$50-$100
1 AV receiver with optical, coax digital, as well as analog inputs ~$100-$200
Total will be around $411-$614, which is competitive with, for example, the current top-end set of Logitech Z906 at $340. Except MUCH LOUDER with better sound quality.
Food for thought