Although tipping does not exist in Japan, you may find yourself charged for things you didn't actually order. Below is a list of the kinds of charges that bars may add to your bill.
Otōshi: Otōshi is a small dish served upon ordering your first alcoholic drink. There charge is typically 200-500 yen per person, and at cocktail bars the dish is generally some sort of bar food like nuts, olives, or smoked ham. Technically speaking it's within your legal rights to decline the otōshi but it's also within the bar's legal rights to not serve you as a result. Some bars, recognizing that otōshi doesn't exist outside Japan, will directly ask non-Japanese customers if they want otōshi or not. This is of course up to you, but since they're the ones asking, this shouldn't impact the quality of service you receive.
Seating charge: This is essentially an upgraded version of otōshi and tends to be charged by higher end bars. The costs can run as high as 2000 yen per person. The dish you receive in turn should be of higher quality. Generally, the menu will indicate what the seating charge is, if applicable.
Service charge: If you're charged this -- the menu or signage should indicate -- it will be a percentage of your bill, typically 10%. Don't think of this as a tip for your particular bartender or service staff though; this is just extra revenue for the bar.
Late night charge: If you're staying past 11:30PM you could find this added to your bill. Like the above service charge, the menu or signage should indicate. This will likely be expressed as a percentage as well, potentially in addition to the service charge. When in doubt just ask for clarification.
Music charge: If there's live music, there could also be a music charge on your bill. Unlike the other charges listed above, the staff will let you know directly if this is to be charged. Pay attention since it could cost quite a lot.