Copán Ruinas [1]’s hippest budget accommodations are at 
En la Manzana Verde (tel. 651-4652, $4 dorm bed), a clean hostel two blocks north from the park where you’ll find 18 beds in dorms named after personalities the likes of Fred Flintstone, 18 Rabbit, and Al Bundy, each with its own footlocker. There are two shared hot-water bathrooms. Guests have use of the kitchen (with fridge) as well as a TV lounge and hammocks. There are daily shuttles to Antigua and Guatemala City ($12) and you can book tours to Finca El Cisne [2] with its nearby hot springs and mountain trails for horseback riding. The hostel is run by the same Belgian owners as the Café Via Via.
Another fine choice in this category is Hotel Los Gemelos (one block east and half a block north of the park, tel. 651-4077, $9 s/d), a popular backpacker spot centered around a pretty courtyard with orchids and run by a wonderful woman who keeps it spotless. She prefers her guests to be back at the hotel by 11 p.m. All rooms have shared bath. There are daily noon shuttle van departures to Antigua.
You’ll have to walk a few blocks southwest of the plaza to find the Iguana Azul (tel. 651-4620, www.iguanaazulcopan.com [3], $4 dorm bed, $11 d), but it will be well worth it. There are excellent-value dorm beds and private rooms sharing a hot-water bathroom. The same Honduran-American owners run the beautiful La Casa de Café next door.
Links:
[1] http://www.moon.com/destinations/guatemala/el-oriente-and-izabal/copan-ruinas
[2] http://www.moon.com/destinations/guatemala/el-oriente-and-izabal/copan-ruinas/sights/finca-el-cisne
[3] http://www.iguanaazulcopan.com