Which notes harmonize with E and what might be a good note to play outside of the key of E for a dissonant effect?
The notes that harmonize with the key of E major are:

-   E - the tonic or keynote
-   G# - the major 3rd above E
-   B - the perfect 5th above E
-   D# - the major 7th above E

To achieve a dissonant, outside-the-key effect, you could play:

-   F or F# - a minor 2nd or major 2nd interval above E, which would create a dissonant clash
-   A - a minor 6th interval above E, which is also dissonant and outside the key of E major

Playing notes a semitone or whole tone away from the notes in the key of E will create tension and dissonance. The further away from the key you get, the more discordant the effect.
What are some examples of songs that use this successfully
There are many songs that use dissonance and tension to great effect, which include:

1. Purple Haze by Jimi Hendrix - This song features a guitar riff that frequently uses the dissonant interval of a tritone (augmented fourth/diminished fifth), which creates a sense of tension and unease throughout the song.

2. Paranoid Android by Radiohead - This song uses dissonant chords and intervals throughout to create a sense of unease and disorientation. The guitar riff in the intro, for example, features a dissonant interval between the notes G and F#.

3. The End by The Doors - The guitar solo in this song features many dissonant and outside-the-key notes, including a prominent use of the blues scale which incorporates the flat 5th interval.

4. Sweet Child O' Mine by Guns N' Roses - The iconic intro riff to this song features a dissonant interval between the notes B and C, which helps to create a sense of tension and anticipation before the song kicks in.

5. Symphony No. 5 by Beethoven - The famous opening four-note motif of this symphony features a dissonant interval between the third and fourth notes, which helps to create a sense of tension and drama throughout the piece.