Public Transit

First: do you need a car here?

That depends on where you need to go, how often, and a few other factors. You can get just about anywhere in Portland proper on mass transit. The suburbs? Results may vary. The best bet is to map your common routes, and see how good the access is.

Trimet: Light Rail, Bus, Trolley

Trimet is the umbrella agency for light rail (MAX trains), trolleys, and regular old buses. The Trimet website has a pretty nice trip planner. Space permitted, you can bring your bike on all Trimet transit. One Pass To Rule Them All, also known as the Hop Card, gives you access to all these forms of transit. You can re-up the card online.

Light rail, aka, the MAX

Within the city, MAX does a great job of moving you along a few primary corridors. However, numerous parts of the city are not reached directly by light rail.

Bus

The city offers numerous bus lines that can move you just about anywhere. The main disadvantage to the bus is that it can be slow, with less frequent service at night. 

Often, it's easy to match or beat the bus by taking your bike.

Bus + Bike or MAX + Bike

All buses have a rack for two bicycles on the front. This is really convenient if you want to ride your bike in one direction but use the bus for a return trip, or if the weather changes abruptly. You can also bring your bike on the MAX if it's not super crowded.

FX2 Superlong bus

Portland recently added the "FX2" bus line, featuring extra long articulated buses, a rapid line from downtown all the way to the suburb of Gresham. I've ridden these buses in Los Angeles, and can confirm they don't actually wheeze like an accordion when going around corners.

Trolleys

I don't have much to say about the trolleys, as I hardly ever ride them. They serve a limited area, but if you are on their route and need to get from point A to point B, they should do just fine.