I bought an older house and some of the wiring does not have the ground wire.
Since the white wire goes to the ground in the breaker box,can I just use it to carry the ground also? Will this be safe?
I have done some of the plug-ins with a jumper wire to the ground and white wire,have I gotten this wrong?
Thanks for any good advice on this.

Yes, you got it dangerously wrong. This is not an acceptable or safe practice.
Grounds must not touch neutrals outside the main panel or disconnect.
It is late so hopefully someone else will be along to expand on this.

You need to remove all of those jumpers. That practice is very wrong, not allowed, and can cause serious issues.

Replacing two wire receptacles with three wire can only be done if certain conditions are in place:

1. Protect the entire receptacle circuit with a GFI circuit breaker, and label each 3 wire receptacle with " No Equipment Ground".

2. Use GFI receptacles at each new receptacle and label with " No Equipment Ground".

3. Use one GFI receptacle at the beginning of the circuit to protect the remaining receptacles in that circuit and label each 3 wire receptacle with " No Equipment Ground".

All of the above will provide for ground fault protection but there is no equipment ground, users need to be aware of, as some equipment, such as surge protectors will not operate properly with no equipment ground.

4. Run new cable to each receptacle that contains an equipment grounding conductor.

There is an allowance that involves running just an equipment grounding conductor to each receptacle and grounding back at the service.

My position is if a grounding conductor can be installed, then new cable can be installed.

As Stan has said, connecting the neutrals and grounds together anywhere passed the main service disconnect can create dangerous conditions... The Electrical Codes go to great length to forbid this and only allow few exceptions.

You say you have an older house, so likely you have two conductor cable (with a black like asphalt jacket or knob and tube), some solutions to this situation can be found in the National Electrical Code 2008 in article 406.3(D)(3)... you can use "two prong" receptacles like you probably already have or if you wish to install three-prong receptacles you have the option of installing a GFCI (ground fault circuit interrupter) to replace the two-prong receptacle. If you do, you must mark the GFCI receptacle "No Equipment Ground".

If the GFCI is installed at the beginning of a circuit with multiple outlets you may now replace the two-prong outlets downstream with three-prong outlets as long as you mark them, "GFCI Protected" and "No Equipment Ground". This is the method that makes the most sense in my opinion from a cost perspective.

Please be careful this is done properly... getting a permit and review by your electrical inspector will affirm you've done this correctly.

I do want to thank each of you for your answers on this.It looks like the ground fault protectors or the way for me to go on this. Thanks again