Israelis Singing in English
As a general rule, I would suggest that Israeli artists try to limit the amount that they sing in English. That being said, there are a number of Israeli artists who have sung in English at various times for various reasons. In the late 60s and early 70s, Israelis covered some (mostly Beatles) songs, such as Arik Einstein's version of "Here There and Everywhere," which were not too terrible. A beatle-esque song called "To Be Alone" appeared on the "Fourteen Octaves" album by Yoni Rechter and Anver Kenner which is actually quite nice. Covers of English songs or original compositions written in English by Israeli artists can sometimes work out, but Israeli artists run into serious trouble when they try to translate their songs into English. This phenomenon can be exemplified by two bands, Kaveret and T-Slam.
In 1976, Kaveret toured the US following their overwhelming success in Israel. They translated their songs into English and were met with a mostly Jewish audience who were interested in hearing the songs in the original Hebrew. On a similar note, T-Slam, a very successful Israeli band from the 1980s tried to translate their hit song and title track from their breakout album "Loud Radio." While the Hebrew Radio Hazak is awesome, the lyrics and cadence of the English version are severely lacking. (T-Slam also gratuitously covered "Smoking in the Boys Room," which probably shouldn't have been made.)
Many Israeli artist feel that singing in English will allow them to break out into a more international market. Arik Einstein's backup band, The Churchills tried to make it in Europe, although they never caught on, even after they changed their name to Jericho Jones. Their work within Israel was with the most influential artist of their time, but in England, they were just another struggling band trying to make music that fit in with the general sound of the time. There are very few bands that succeeded in the broader music market either in Europe or the US. A notable exception was Minimal Compact, a punk band, which was formed by Berry Sakharof in Amsterdam in 1981. They became popular throughout Europe and their fame grew in 1984 when they were joined by Sakharof's old buddy from Tel Aviv, former Tammuz roadie and original Israeli punk rocker Rami Fortis. Throughout the 80s, the band enjoyed a modicum of success in Europe, and toured the old world from Spain to Japan, but never realized their ambition to tour America because US immigration would not let them into the country. Sakharof is still an influential force in Israeli music, and Fortis' 1978 album, Plonter, is still a powerful listen after all these years.
On the other hand, there are quite a few bands in Israel today who only perform in English. Many are on the independent scene, and seek to break out of Israel and gain broader popularity. Some of these current artists might even make it; the energetic and charismatic Shy Nobleman, and eclectic DJ, MC Karolina. I personally like an album called Chameleon Mood Swing by Lemmus Lemmus, which is end to end psychedelic goodness in the style of Pink Floyd. A Neil Young-like Israeli band called The Flying Baby that exclusively sing in English recently toured the US. Rockfour is a band that actually did make it; initially they sang in Hebrew, but three albums into it they started singing in English and the band now tours the US regularly.
If you happen to be in Israel and are interested in seeing a great live band that sings in English, I have two recommendations. First is Funk'n'Stein, an eight member funk ensemble. Their CD comes with an invitation to a live show, where like any good funk band, they improvise on their songs and take the audience along for a funky good time. The other band is called Southbound Train, or SoBo to those "in the know." SoBo is the resident band at Mike's Place and is fronted by one of the owners Assaf Ganzman. Then again, Mike's place is a live blues bar with locations in Tel Aviv and Jerusalem, and even if SoBo isn't playing, you'll still have a chance to hear some great live music.
To further confuse everything written in this section, check out the song "Hebrew Man" by Ehud Banai. I can't find a YouTube version of it, but I suggest getting his 2004 album, "Answer Me" (Ane Li) which has the "Hebrew Man" as well as other Cannanite blues songs.
Here's a great lesson plan written by Robbie Gringras that uses the song as jumping off point for experiential education.
Shy Nobleman - Baby In the Rain
Same video off of Shy's site. It's a smaller size but better quality.
Rockfour - Astronauts
Trailer for a documentary on Minimal Compact (With English Subtitles)
SoBo, live at Mike's Place in Tel Aviv performing "Girl From Mandalay"
Mike's Place Website
MySpace Pages for Israeli Artists Who Sing In English: