There are numerous distance indicators used for within the galaxy. The most common way is by using intrinsic magnitude. By knowing how bright an object would be if we were close, we can determine how far away it is by how dim it is. There are many types of stars where we have a rough idea of how bright they should be due to characteristics of the star:
1. Cephied Variables: The original type of variable star that was used by Hubble to determine the distance to the Andromeda Galaxy.
2. RR Lyrae Variable: Like the Cephied variable, but usually dimmer.
3. Type 1a Supernova: These guys, unlike the first two, are cataclismic variables. 99
Essentially a binary white dwarf slowly accretes matter from its binary till it reaches the Chandrashankar Limit, after which point it explodes in a very characteristic way (since the mass at the time of explosion is roughly constant).
4. Main Sequence Stars: Generally less accurate than the first 3, there are some types of main sequence stars which are used to find distances in a similar way.
There are a few other ways we can measure distances:
Perpendicular Movement: For example there is a "light echo" from SN 1987A which is essentially light from the supernova interacting with dust around the old star. Since this echo should be expanding at the speed of light, we can tell how far away the nova is by the angular velocity of the light.
Relative Velocity in a Moving Cluster: (see <PERSON>'s answer)
Tulley-Fisher relation: A relationship between the luminosity of the galaxy and it's apparent width. Can be used as a decent distance calculator.
Faber-Jackson Relation: Similar to Tulley-Fisher, relates luminosity with radial velocity dispersion rate.
EDIT: Some more information about redshifts.
The whole relationship between redshift and distance was in fact established by Hubble by relating distance to Cephied variables (I believe) with redshift. Later on it was made more precise using supernova, which are brighter and can be seen from much father away (I think recent supernova can be occasionally seen around Z=2, while Cephieds are all Z<1). Within a galaxy, redshift cannot be used directs since the "peculiar velocity," the velocity within the galaxy, completely overshadows the effects of universe expansion on which Hubble's Law is based. Redshift within the galaxy is useful for certain other techniques.
EDIT: corrected a few minor errors. 562