Hulu Plus occasionally offers a 2-week trial. Normally, it's one week, but they're running an ad on the My Channels page for two weeks free. Also, any Hulu Plus subscriber can send you a link for a 2-week trial, if the ad special stops before your Roku arrives.
Netflix offers a one-month trial. That's their standard.
Your best bet for those channels is to sign up for the free trials.
Amazon Prime offers a one-month trial. That's their standard. However, you can browse Amazon Prime wihout a Prime account. Just look for the Prime inidicator on shows. You can also filter by "Prime" when browsing. Of course, non-Prime content is available for purchase.
Roku 3, Roku LT
Apple TV, TiVo/OTA, FireTV Stick, Chromecast
Roku HDMI Streaming Stick, Roku 1, Roku 2 XS, Roku 2 XD, Roku 2 HD, Roku XD|S, Roku HD