On oversells, they will seek volunteers. Depending on length of delay, they will offer a travel voucher for $100 or $200, plus the value of your one-way ticket and put you on priority standby for next available flight (or confirm you, if space is available). They are often pro-active in oversell situations. While at LAS this week, they paged a couple by name who were booked LAS-DEN-MDW, as LAS-DEN was oversold. They offered the couple the MDW non-stop arriving only 10 minutes later than their connection would have arrived at Midway, plus a voucher for $100 + ticket value. The couple accepted and they never had to seek volunteers.
On delays, don't expect anything at the gate. However, there have been numerous reports of inconvenienced passengers subsequently receiving a letter of apology and a voucher for future travel. There is a thread in this Forum on that topic.