One of the key bits of knowledge that you gain after playing Angband for a while is learning when you are too deep compared to your equipment / character level / skill.  At least, if you don't want to suffer from "it breathes... you die" situations.

From the old Angband FAQ (part 1, part 2) which was written for Angband 2.8.3:
  • 1000' - Free Action (paralyze), See Invisible (ghosts, invisible critters)
  • 1500' - Fire/Cold/Acid/Lightning Resists (the basic 4 resists)
  • 2000' - Poison/Nether Resists, Hold Life
Below 1000' and you start running into very nasty critters who can paralyze you or are invisible.  The dragons and other things which breath the basic four damage types start showing up around 1500'.  When you get below 2000' you start running into Drolems with nasty poison attacks along with things that breath/cast nether spells.  The undead below 2000' also like to drain your XP.

Things changed a bit in the 3.0 series and even more in 3.1-3.3.  More current recommendations are that you should have the following before descending below these levels:
  • 1000' - Free Action (paralyze), See Invisible (ghosts, invisible critters)
  • 1500' - Fire/Cold/Acid/Lightning Resists (the basic 4 resists)
  • 2000' - Poison/Nether Resists, Hold Life
  • ???? - Speed of +10 (permanent or temporary)
  • ???? - Speed of +20 (permanent or temporary)
Adjust based on your risk attitude and what character you are playing.  Some of the monsters below certain depths can one-shot kill you without the proper resists.  Some monsters can be easily avoided, others you will run the risk of senseless depth without some form of monster detection (such as telepathy or checking for monsters every 20-40 steps).