Here are some of the separation rules from the ATC regulations;
http://www.faa.gov/ATpubs/ATC/index.htm

The parts below are just a simplification of the basic rules. The actual
rules are quite in-depth and have to consider the actions of the
aircraft involved, the type of flight plan, airspace classification, and
whether wake turbulence will be a factor.


7-2-1. VISUAL SEPARATION

Aircraft may be separated by visual means, as provided in this
paragraph, when other approved separation is assured before and after
the application of visual separation. To ensure that other separation
will exist, consider aircraft performance, wake turbulence, closure
rate, routes of flight, and known weather conditions. Reported weather
conditions must allow the aircraft to remain within sight until other
separation exists. Do not apply visual separation between successive
departures when departure routes and/or aircraft performance preclude
maintaining separation.

a. TERMINAL. Visual separation may be applied between aircraft
under the control of the same facility within the terminal area up to
but not including FL 180, provided:

1. Communication is maintained with at least one of the
aircraft involved or the capability to communicate immediately as
prescribed in
para 3-9-3, Departure Control Instructions, subpara a2 is
available, and:

2. The aircraft are visually observed by the tower and visual
separation is maintained between the aircraft by the tower. The tower
shall not provide visual separation between aircraft when wake
turbulence separation is required or when the lead aircraft is a B757.

3. A pilot sees another aircraft and is instructed to maintain
visual separation from the aircraft as follows:

(a) Tell the pilot about the other aircraft including
position, direction and, unless it is obvious, the other aircraft's
intention.

(b) Obtain acknowledgment from the pilot that the other
aircraft is in sight.

(c) Instruct the pilot to maintain visual separation from
that aircraft.

(d) Advise the pilot if the radar targets appear likely to
converge.

NOTE-
Issue this advisory in conjunction with the instruction to
maintain visual separation, or thereafter if the controller subsequently
becomes aware that the targets are merging.

(e) If the aircraft are on converging courses, inform the
other aircraft of the traffic and that visual separation is being applied.

(f) If the pilot advises he/she has the traffic in sight
and will maintain visual separation from it (the pilot must use that
entire phrase), the controller need only "approve" the operation instead
of restating the instructions.

PHRASEOLOGY-
TRAFFIC, (clock position and distance), (direction)-BOUND,
(type of aircraft), (intentions and other relevant information).

If applicable,

ON CONVERGING COURSE.

DO YOU HAVE IT IN SIGHT?

If the answer is in the affirmative,

MAINTAIN VISUAL SEPARATION.

If the pilot advises he/she has the traffic in sight and
will maintain visual separation from it (pilot must use that entire phrase):

APPROVED.

If aircraft are on converging courses, advise the other
aircraft:

TRAFFIC, (clock position and distance), (direction)-BOUND,
(type of aircraft), HAS YOU IN SIGHT AND WILL MAINTAIN VISUAL SEPARATION.

Runway separation requirements are as follows;


3-9-6. SAME RUNWAY SEPARATION

Separate a departing aircraft from a preceding departing or arriving
aircraft using the same runway by ensuring that it does not begin
takeoff roll until:

a. The other aircraft has departed and crossed the runway end or
turned to avert any conflict. If you can determine distances by
reference to suitable landmarks, the other aircraft needs only be
airborne if the following minimum distance exists between aircraft: (See
FIG 3-9-1 and FIG 3-9-2.)

1. When only Category I aircraft are involved- 3,000 feet.

2. When a Category I aircraft is preceded by a Category II
aircraft- 3,000 feet.

3. When either the succeeding or both are Category II aircraft-
4,500 feet.

4. When either is a Category III aircraft- 6,000 feet.

5. When the succeeding aircraft is a helicopter, visual
separation may be applied in lieu of using distance minima.

NOTE-
Aircraft same runway separation (SRS) categories are specified in
Appendices A, B, and C and based upon the following definitions:

CATEGORY I- small aircraft weighing 12,500 lbs. or less, with a single
propeller driven engine, and all helicopters.

CATEGORY II- small aircraft weighing 12,500 lbs. or less, with propeller
driven twin-engines.

CATEGORY III- all other aircraft.

Gene Whitt wrote:
Jeff,
The 'local' ATC station is responsible for airborne traffic and must
provide 'standard' separation but ACTUAL avoidance is always the first
responsibility of the pilot. They may give advisories and often do but it
is only required when conditions permit.

Once traffic has been pointed out to you and you acknowledge having the
traffic in sight, ATC does not need to advise you ever again. Consequently,
there are times when it is to your advantage
not to tell ATC that you have the traffic.

Happened to me once when ATC told me of a KC-10 on short
final to a runway. I said I had it in sight. What I didn't know was that
it was a touch-and-go and not a full-stop. A bit later it filled my
windshield but ATC he don't say nothin'.
Gene