3m has everything necessary:

http://www.command.com/3M/en_US/command/products/~/Command-C...

http://www.command.com/3M/en_US/command/products/?N=5924736+...

Google "nail in cable clips." A small nail makes a small hole but if you run the cable along a wooden baseboard or molding, the holes aren't really noticeable (not like a hole in the wall from hanging a picture). There are adhesive cable clips but I've never used them, they're probably more expensive especially if they're the "Command(tm)" adhesive that's supposed to come off cleanly.

Properly setup command strip based hooks can work.

However most apartments let you 'hang pictures'; anything that leaves so small of a hole that painting over it effectively patches it.

If your rooms are carpeted, there is actually a gap between the baseboard and the floor. With care you can fit coax or cat5 in there no problem. It ends up completely hidden.