I did some homework and learned that they haven't changed their logo, pretty much ever. I was surprised the logo's font hadn't been updated, but I was pleased. I know this company prides itself on heritage, and time & success have shown what this recognizable, personal touch - as well as consistent top quality - has done for the public's view of the brand.
As it turns out, the logo is not a font, but was based on the handwriting(same link as "pretty much ever") of James Wood Johnson, co-founder of the brand (founded with his brother, Edward Mead Johnson in 1886). His handwriting was a little messy, but personalities like the ampersand connected to the second J are taken into great consideration.
Johnson & Johnson's blog, Kilmer House, has tons of history.
The tape canister couldn't be more simple. It uses red, white & blue, and includes the universal medicine symbol - a red cross. I like how "Adhesive Tape" is in blue on the sides, and white-on-blue on the top. Great uniformity. Also, the bold, all-caps lettering is not only clear (to the shopper's eye from the shelf) but a good, simple contrast to the cursive "Johnson & Johnson" logo. Both pieces of the product are identical on either side of the piece - so no instructions or anything on the other side.
The female half has one end of the metal rolled out, and one rolled inward. The inward-rolled end serves as a blocker for the spindle.. So the only way to put the spindle away is when the tube's logo is upright.
The logo as it appears on their website now: