Weber is largely identified with Freischütz which is not entirely unjustified as no other piece has had such an impact (as the founding of German romantic opera) and lasting popularity. There are, however, two more large scale operas, composed after Freischütz, Euryanthe and Oberon, that contain wonderful music but are dramatically very weak, so they are almost never staged.
He also wrote a few minor stage works (the Turandot music is an early attempt at exoticism, Hindemith used a "chinese theme" for his Metamorphoses) and a surprising amount of instrumental music. Lots of piano music because before becoming an important opera composer he was one of the most famous virtuosos of his day. The best concertante pieces IMO are the f minor clarinet concerto and the Concert piece for piano in the same key. But the two piano concertos are also worthwhile, close to Beethoven but less heroic and with more virtuoso fireworks. The other clarinet etc. concerti are nice but not that essential, unless one is fond of woodwind concerti. Same for the chamber pieces (a trio with flute, some violin sonatinas and a couple of virtuoso clarinet pieces) The two symphonies are very early pieces and interesting but don't expect anything close in style or weight to the famous ouvertures.
Of the piano solo music the best known piece is Invitation to the dance which is basically the beginning of the concerto waltz; this one used to be far more popular in earlier times, both the original and Berlioz' orchestration. There are 4 piano sonatas (Richter played the 3rd, I think, and several other famous pianists have recorded the 2nd or 3rd), nice pieces but all a bit too long for me. (Very roughly, think of a more shallow, loosely built version of a Schubert sonata with lots of virtuoso fireworks added.)
He also wrote songs and choral music (two masses) but I don't think I have heard any of this.
