TITLE: Recommendation on stochastic process books
QUESTION [15 upvotes]: I was wondering if someone could recommend good books on stochastic processes 

with measure theory treatment
with not much or no measure theory
treatment

for each, it would be nice to have some books for introductory level, mid-level to comprehensive level respectively. They can be either classical or recently published, either continuous, discrete or both.
Thanks in advance!

REPLY [10 votes]: Some good books include:

Stochastic Processes by Sheldon Ross (no measure theory)
Introduction to Probability Models by Sheldon Ross (no measure theory)
Stochastic Processes by J.L.Doob (measure theory)