The best replacement for dial up is dsl.

The best alternatives to dial up are rated as following:
★★★★★  dsl
★★★★★  broadband
★★★  high speed
★★  vpn
★  isdn
★  broadband speed
★  leased line
★  dsl speed
★  adsl
★  high speed internet
★  satellite internet
  cable internet
  dsl speeds
  vpn remote access
  yahoo dsl

Your alternative for dial up is not listed? Suggest!
Speaking about dial up, one probably shouldn't forget about wireless router.

Other search terms related to dial up and their ratings are:

★★★★★ wireless router
★★ call waiting
★★ xbox live
You have in mind a companion for dial up and it is not yet here? Propose!

Google Trends

Scale is based on the average worldwide traffic of dial up in all years. Click on graph for more.
dial up