Meteo Qt is a tray application that displays the current weather temperature on the panel, with a 6-day forecast easily accessible from its menu. 

Meteo Qt in Kubuntu 17.04

The application is based on Python 3 and Qt 5, and while it is aimed at Qt-based desktops (like KDE Plasma or LXQt), it works pretty well on GTK-based desktops as well (either as a tray or as an AppIndicator).

wttr.in is a web frontent for Wego, a weather app for the terminal. Using nothing but cURL and wttr.in, you can get weather information from a terminal, without having to install anything (well, except for cURL).

My Weather Indicator, an Ubuntu AppIndicator for displaying the current weather on the panel, was updated to version 0.6.8 today, receiving numerous bug fixes as well as a few other changes.

My Weather Indicator and one of its optional desktop widgets

Weather Indicator used to be one of the most popular Ubuntu appindicators but unfortunately, it doesn't work properly any more: it crashes when trying to add a new location and the weather forecast doesn't work - because of this, it was even removed from the Ubuntu 13.04 (Raring Ringtail) official repositories.

However, if for whatever reason you don't want to use My Weather Indicator, a pretty cool alternative by the way, you can now use Weather Indicator again thanks to Joshua, who has fixed the two issues mentioned above along with some other bugs and has created a PPA so you can easily install a working Weather Indicator in Ubuntu 13.04, 12.10 and 12.04.

`My Weather Indicator` is an Ubuntu AppIndicator which displays the current weather in the top panel. The application comes with many features, including weather forecast, a cool forecast map and even desktop widgets.

Because of API limitations, Wunderground and World Weather Online didn't work properly in My Weather Indicator lately, so a new version has been released recently which allows users to enter their own API keys for these services in the My Weather Indicator preferences.

You can continue to use Open Weather Map and Yahoo weather services, which don't require you to enter an API key, so this isn't something required to get My Weather Indicator to work, it's just if you want to use Wunderground or World Weather Online services.

My Weather Indicator has got widgets support a few days ago, but I didn't write about it back then because it was the initial widgets release and there was still work to be done. 

Today, the application has been updated, adding 3 weather widget styles along with options to display the widget on top (or under), or to hide the indicator when the widget is displayed: