The Buenos Aires subway/metro system, known as the Subte, is modern safe and somewhat efficient. Avoid taking inbound trains during the morning rush hour and outbound ones during the evening rush hour. This particularly applies to the C (line) which can be difficult to board from downtown in the direction of Constitución during the afternoon. During the summer the the stations can be quite warm.

The first trains leave the end of the line at 5AM (8 AM Sundays and holidays) while the last train leaves the end of the line between 10:20 and 10:50 at night (Sunday 20 minutes earlier). The premetro is on a slightly different schedule.
Fares

1.10 pesos to go anywhere. If you plan on using the subte more than once, and chances are you will, buy a Subtepass card for 2, 5, or 10 trips. The lines at the ticket counters can be annoyingly long and slow.

A map of the routes can be found here: Map of Subte

The subte was the first subway in South America and is a bit of a tourist attraction in itself. The interior of the cars of the A line (the light blue one) are beautifully decorated in wood. So if you are on Avenida de Mayo and looking for something different, head underground and take the A line to Caballito. Here’s a video of a trip on the A line: