System designers usually protect systems from overcurrent to avoid liabilities from house-fires. So you normally can't damage USB ports - there is either a polyswitch (resettable fuse), or electronically-limited "high-side" switch that would self-disconnect if the load current exceeds the set limit.
Regarding how much current a port on a mainboard can supply, USB specifications call for "at least 5 units of load", each unit being 100 mA (150mA and six units for USB3.x). Typically the overcurrent threshold is 40-50% higher than the minimum from specs, to accommodate for circuits production variability. So an average USB 2.0 port may deliver 900 mA without causing any USB issues, and the connector won't melt down (typical current rating of USB connectors is at least 1.5A). However, some product samples might be marginal and work "half-way", randomly disconnecting and recovering back. So it is up to your definitions of what is "bad" and what is not.
Regarding "low ampage supply" to plug into "high ampage device", it is an entirely different story, and this kind of mismatch will likely cause some power starvation somewhere in the device and a malfunction of it. Typical example would be SATA 2.5" HDD USB enclosures that can consume something like 1.8A peak currents from cable during spin-up or active track search, and sagging voltage would prevent the HDD to be recognized by USB-SATA bridge, and this mass storage device would fail enumeration.