Every legal resident living in the United States for at least half a year before any given election should have a right to vote in federal, state, and local elections regardless of citizenship status.
As a US Citizen, I can voice opposition to how my tax dollars being spent by voting against those who claim to be my representative in government, but my resident alien friends and coworkers who just happened to be born in a different country than their dream job was located (where they may be making more than me and thus even paying more taxes than me - often to both the United States and their native country) have no such venue for feedback to representatives.
We should at the very least give resident aliens a voice in how their tax dollars are spent as is the case for some countries.