“Companion Planting is the growing together of all those elements and beings that encourage life and growth; the creation of a microcosm that includes vegetables, fruits, trees, bushes, wheat, flowers, weeds, birds, soil, microorganisms, water, nutrients, insects, toads, spiders, and chickens.” – John Jeavons, How to Grow More Vegetables Than You Ever Thought Possible
Good candidates to companion plant with peas are Squash – when squash follows peas up trellis. Lettuce, radishes, carrots, turnips, cucumbers, corn ,beans, spinach .
Avoid all onion family plants particularly Garlic, as they are proven to stunt peas growth and vice-verse. .
Sweet peas will attract pollinating insects which helps with open pollinated plants. Flowers such as sweet alyssum, roses, lavender will benefit from being in the vicinity of sweet peas
Peas will be hampered when they are too close to Gladiolus – Peas don’t fare well with gladiolus. Peas are cool-season vegetables , gladiolus bloom in the summer, the gladiolus bloom begins at an inconvenient time, while the peas are still producing and robs essential nutrients stifling their development.
Other flowers in the lilly family should also be kept a safe distance from peas for the very same reason, as well as the fact that they are bulbous and it is suggested that some cultivars, exhibit the same semi-alleopathic behavior as alliums.
Avoid planting peas too close to Tomatoes. Peas are carriers of Fusarium Crown and Root Rot. The majority of the time they can be grown together with no detrimental effects, but statistically – if you keep inter-planting them it will eventually come back to bite you in the butt. 
Avoid Fennel which is allelopathic to most garden plants. It exudes compounds designed by nature to eliminate competing plants from its immediate area. Dill is one of the few garden crops that can be grown with it.
Peas can be successfully grown with early Potatoes. They repel the Colorado potato beetle. . However – Avoid planting them with or near late season potatoes, for the same reasons you avoid planting them with Tomatoes , which are close relatives of potatoes.
Onions all emit a pungent aroma which repels many insects. Garlic, a related crop, also releases sulfur into the soil that is beneficial to Tomatoes and detrimental to soil borne pathogens. Onions and alliums will repel nearly all varieties of aphids.
Squash and peas make good candidates for companion planting when using a trellis. Early peas are best, they will climb the trellis while the squash is maturing at the bottom. The peas will be harvested or harvestable and have fixed some nitrogen in the soil for the squash, which will then follow the peas up the trellis.
Spinach is sometimes suggested as a companion for peas. They will grow together just dandy and there are no notable antagonistic effects other than competition for resources when grown too close.
Legumes and Beans which include peas grow well with lettuce. In one study Okra and Lettuce + Squash and lettuce planted in conjunction with beans produced yields of 45 -66% higher than those of beans planted by themselves. 
God’s Garden, My Life – Bonnie J. Lee
Peas grow well with Carrots due to the nitrogen fixing properties of the peas which theoretically help to satiate the nutrient requirements of carrots. Carrots however are not heavy feeders , they don’t require excessive nitrogen so although the peas and legumes planted with carrots is not a bad thing, it doesn’t do a whole heck of a lot for the carrots.
The Carrots however act as a deterrent for some pests that hinder Peas and some related crops. Bush Beans – ditto … Snap Beans – ditto … Green Beans – ditto …
Experience has taught me that cucmbers and peas do not fare well together as the competition for space and the vines intertwining and strangling each other out outweighs the advantages – UNLESS- you time it correctly [See Squash above].
3. Peas were shown to reduce the density of Colorado potato beetles — Mateeva, A.; Ivanova, M.; Vassileva, M. (2002). “Effect of intercropping on the population density of pests in some vegetables”. Acta Horticulturae 579: 507-511.