You can buy nipple guards and most running specialty stores, I found that these stick better than regular band-aids. I have also used duct tape which stays on even during heavy sweating (we do a lot of that here in Florida)...removing the duct tape is quite fun after the race 

I stick with regular bandaids and have never had trouble.  Like ctxcrossx said, you need to put them on at least 10 minutes before you start sweating if you don't want them to fall off. Otherwise, it's a crapshoot.

I've heard good things about body glide, but I have never used it. Same goes with the nipple guards which are basically small band aids with better adhesive.

You can try two bandaids in a crossing pattern over both nipples; generally speaking, at least one stays on. That is how I manage them when I forgot to put the bandaids on until right before the race or long run.

I like the duct tape idea...although you might want to use a bandaid for the nipple itself under the duct tape if you go that route! I've never tried it though so I can't say for sure.

Another option is to wear a different shirt.  Wearing cotton on a hot day is just asking for trouble.  Most technical fabrics will be a bit more forgiving, although I try to remember the band aids whenever possible.

A few tips I've learned...

Body glide works well for me for shorter runs (1-2 hours, depending on the heat), but longer runs I always use bandaids.

Get the kind that have a somewhat "fabric" feel, not all plastic. They seem to give a bit more and stretch. Personally I think they stick a lot better too (either store band or "BandAid" brand), I think they are often marketed as "flexible" and sometimes even "sport" band-aids.

Apply vertically. That way, the only edge that your shirt can rub on is the part in contact with your skin and has adhesive on it. If you put one on horizontally (or if the outer one is horizontal when using 2 criss-crossed), the edge of the part that doesn't stick can catch on your shirt and is much more easily ripped off.

Don't apply too tightly. If there is no room to flex your chest muscles, they will come off more easily (I learned this the hard way on a long run that also included multiple "fitness stations". The pullups ripped the bandaids right off!)

Kinda goes without saying, but the bigger the bandaid, the more area to adhere. I find the 3/4 inch wide ones work well.

I've also heard of people using sport tape, the kind that is used to wrap ankles, etc. It sticks very well (and can be had for cheap), but be sure to use gauze or something over the actual nipple area, or you'll be sorry.

Crazy Glue and cotton balls.

Look for;

BAND-AID Tough-Strips that say Heavy Duty Fabric on the front of the box.  These are old style, fabric backed band aids.  I sweat a lot and they stay on, even for a 100 miler.

I almost didn't read this post because I thought it would simply be a big advertisement for Body Glide Great suggestions with all the other ways. I can say that as a person who sweats profusely during a run, until I started using Body Glide on the nipples I, too, ran into problems with band aids, tape, etc. So I highly endorse Body Glide, just don't mistake it for your deodorant, done that a few times and you end up stinky with a very odd lubricated sensation under the arms!