Obviously there are a fair number of commons and uncommons that are played heavily in modern. As a result they are surprisingly valuable, considering their rarity. Some examples:

Inquisition of Kozilek(Rise of the Eldrazi uncommon): ~$15.00
Gitaxian Probe (New Phyrexia common): $3.91
Terminate (Alara Reborn common): $3.44
Relic of Progenitus (Shards of Alara common): $3.45
etc...

Would any Modern players out there mind listing any valuable commons and uncommons that they are aware of?

The easiest way to look is right in front of you using Deckbox :)

Click on Card Database
Change Format to Modern
Add More Filter - Rarity
Select Common and Uncommon

Apply Filters

Click on Price to sort.

Not all of them, I don't think, are heavily played in Modern - but a lot are!

I hope this helps

Thanks! I'm new to this ;)

I also found this great link:

http://blog.mtgprice.com/2014/10/27/the-great-modern-uncommon-and-common-search-data-crunching-part-2/

Here is a link to the search that Krazy mentioned:

http://deckbox.org/games/mtg/cards?f=b35%21633.2&o=d&p=1&s=i