TL;DR: No, there isn't.
JR is a group of independent companies that do a pretty good job of running trains together, but don't really collaborate on ticketing and reservations, so there is no centralized all-JR reservation system.
The closest to this is JR East's Ekinet, which allows booking tickets more or less anywhere in the country, but it's Japanese-only, has a moderately complicated sign-up process that requires a credit card and a Japanese address, and above all, requires that any reserved tickets be physically picked up at JR East stations, meaning the Tokyo area and points north only. If you're starting your trip outside Tokyo, as I presume you are since you're asking about JR Central & West, tough cookies. Now Ekinet does have a little English section aimed at overseas visitors, which has less hoops to jump through, but only allows booking JR East trains. As far as I'm aware, this is the only English-language service available.
JR Central and West have a similar Express Yoyaku service, covering the Tokaido & Sanyo Shinkansens only (no non-Shinkansen express trains). However, the same limits apply and it costs ¥500/1000 per year to boot. Plus you need to pick the more expensive service if you want to book tickets for people other than yourself.
Last but not least, JR West, JR Kyushu & JR Shikoku operate another shared service with the catchy name of e5489 (read ii goyoyaku, or "good reservation"), which lets you book the Sanyo & Kyushu Shinkansens plus all express services in the tri-JR area. And I'm sure you'll be astonished to hear that this, too, requires signing up to be a "J-WEST Net" member in Japanese with a Japanese address.
All that said, I wouldn't fret too much. You can make reservations for any JR train in Japan quite easily in person at any JR station once you've landed. More importantly, though, reservations are only necessary at absolute peak periods (New Year's, Golden Week, Obon, maybe Friday nights for Tokyo<->Osaka), 99% of the time you can get unreserved seats or, for reservation-only trains, reserve a seat on the spot.