1. If possible, dedicate the Programming Clock and Data pins to ICSP.  If you must also use these pins for other purposes on your board, some thought should be given to the type of hardware that is connected.  The best case is to use the programming pins for normally-open, pushbutton inputs.  As long as you don't push the buttons while programming, the switches won't affect things at all.

If loads are connected to the clock and data lines, they must not interact with the clock and data signals.  Capacitive loads will cause problems.  High-impedance loads are usually ok.  LEDs with current-limiting resistors are less desirable, but usually don't cause problems.

You should always prototype and test the ICSP connections before sending your PCB design out for fabrication.

2.  The MCLR pin on the PIC will be driven to approximately 13V during programming.  This raises two concerns.  The first is that your circuit must allow 13V on the pin.  Don't connect the pin directly to the Vdd rail.  The second concern is that the rest of your circuit may need to be protected from this voltage.  If 13V on the MCLR pin might put at risk other components on your board, use a diode in series with the RESET pullup to keep the 13V off of the Vdd line.
  

In some situations, there just aren't enough pins to allow the use of a RESET.  Your project will require that MCLR be used as an input.  This is common on small, 8-pin PIC MCUs.  In these cases, it helps to set the clock and data pins to inputs and place a delay at the beginning of your code.  This will allow you to cycle power to the part and start the programming process while the pause is executing.

In a PICBASIC PRO program intended for the PIC12F675, you might start with:

TRISIO = $FF   ' set all pins to inputs
PAUSE 1000     ' wait a second

This can make reprogramming much easier to accomplish when the programmer has no means to reset the target device.  
 

5.  Always connect every available power pin to the appropriate power or ground source.  Many PIC devices have multiple pins that are labeled Vdd, Vss, AVdd, and AVss.  If even one of these pins is left unconnected, it may result in programming errors.  This applies to analog supply pins even if you don't plan to use the analog functions.
 

7.  Connect a 5V supply to the Vdd pins on the PIC.  You can do this with the normal power supply on your board or with an external supply.  The ICSP header on the programmer has a 5V pin (pin-1) that can be used, but only if your board doesn't consume too much power.  The Vdd pin (pin-4) on the header shouldn't be used.  Such use will probably cause errors during programming, and it's possible that it will damage the programmer hardware.

If your board is designed to run at a lower supply voltage like 3.3V and you can't safely connect 5V to the PIC, you may have issues when erasing a flash PIC.  For some devices, a low-voltage erase option is available (Options > More Options in the meProg software).  Do not enable low-voltage programming in the configuration settings!  This setting has nothing to do with the supply voltage for the PIC.

Some of the new PIC microcontrollers cannot by powered at 5V.  These parts usually require additional circuitry for in-circuit programming.  See the following link for details:  PIC18FxxJ, PIC18FxxK, PIC24xJ, and dsPIC33FJ 3.3 Volt Programming Information

Note for PIC17C7xx:  These (practically obsolete) devices may also be programmed in-circuit. However, different pins are required than are detailed here.  See the Microchip programming spec on these devices for more information.