The 2013 Interactive Fiction competition is currently ongoing: http://ifcomp.org/comp13/info.php

It has a variety of fairly short games playable online, some being parser-based (you enter a command and the world tells you what is happening) and some in other forms (e.g. Twine games, where there's a clearly marked set of things you can do at each node, CYOA-style), some puzzly and some less puzzly. Here is a brief introduction to parser-based IF if you find yourself confused.

I enjoyed:

• Captain Verdeterre's Plunder by Ryan Veeder - a short puzzle game with an entertaining narrative voice, where you rush to scrounge up valuables from your sinking ship and make it off alive.
• Their Angelical Understanding by Porpentine - a moving allegorical story about something like pain and redemption.
• Coloratura by Lynnea Glasser - where you play a strange, inhuman mind which can emotionally influence humans to try to get them to achieve your goals.
• Solarium by Alan DeNiro - an alternate history about nuclear holocaust with fantastic elements.

Additionally, if you play them and have an opinion then you can sign up and vote afterward :-)